MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 01
STRAIGHT LINE
TOPIC : DISTANCE FORMULA, SECTION FORMULA, SLOPE OF LINE & ANGLE BETWEEN
TWO LINES

1. The angle between the lines 2x + 3y = 5 and 3x – 2y = 7 is-

(A) 45º (B) 30º (C) 60º (D) 90º

2. The coordinates of a point are (0, 1) and the ordinate of another point is –3. If the distance
between the two point is 5 then the abscissa of another point is-
(A) – 3 (B) 3 (C) ± 3 (D) 1

3. The three points (–2, 2), (8, –2) and (– 4, – 3) are the vertices of
(A) an isosceles triangle (B) an equilateral triangle
(C) a right angled triangle (D) none of these

4. If x-axis divides the line joining (3, 4) and (5, 6) in the ratio  : 1 then  is-
3 2 3 1
(A) – (B) – (C) (D)
2 3 4 3

5. The points which trisect the line segment joining the points (0, 0) and (9, 12) are
(A) (3, 4), (6, 8) (B) (8, 6), (0, 2) (C) (1, 3) (2, 5) (D) (4, 0), (0, 3)

6. A point on the line joining points (0, 4) and (2, 0) dividing the line segment externally in ratio 3
: 2, is -
3 8 8 3
(A) (3, –4) (B) (6, – 8) (C)  ,  (D)  , 
5 5 5 5

7. P and Q are points on the line goining A(–2,5) and B (3,1) such that AP= PQ = QB. Then the
mid point of PQ.
1   1 
(A)  ,3  (B)   ,4  (C) (2, 3) (D) (1, 4)
2  2  

8. The ratio in which the join of the points (1, 2) and (– 2, 3) is divided by the line 3x +4y = 7 is-
(A) 4 : 1 (B) 3 : 2 (C) 3 : 1 (D) 7 : 3
: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-1
9. If A (2, 3), B(3, 1) and C(5, 3) are three points, then the slope of the line passing through A
and bisecting BC is -
(A) 1/2 (B) – 2 (C) –1/2 (D) 2

10. Slope of line joining points (5, 3) and (k2, k + 1) is 1/2, then k is
(A) 1 (B) 1 + 2 (C) 2 –1 (D) – 1 – 2

11. If the points (k, 2 – 2k), (1 – k, 2k) and (–k –4, 6 – 2k) are collinear, then possible values of k
are
1 1
(A) – ,1 (B) ,–1 (C) 1, 2 (D) 1, 3
2 2

12. Slope of line bisecting the angle between co-ordinate axes, is

(A) ±3 (B) ±2 (C) ±1 (D) ±5

13. Find the distance between the points (a cos , a sin ) and (a cos , a sin ) where a > 0.

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-2
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 02
STRAIGHT LINE
TOPIC : VARIOUS FORMS OF LINES

1. If the point (5, 2) bisects the intercept of a line between the axes, then its equation is-
(A) 5x + 2y = 20 (B) 2x + 5y = 20 (C) 5x – 2y = 20 (D) 2x – 5y = 20

2. Equation to the straight line cutting off an intercept unity from the positive direction of the axis
of y and inclined at 45° to the axis of X is -
(A) x + y + 1 = 0 (B) x – y + 1 = 0 (C) x – y – 1 = 0 (D) x – y + 2 = 0

3. If a straight line passing through (x1, y1) and its segment between the axes is bisected at this
point, then its equation is given by
x y x y
(A)   1 (change) (B)  2
x1 y1 x1 y1
(C) xy1+ yx1 = 1 (D) 2(xy1+yx1) = x1y1

4. Find equation of a straight line on which length of perpendicular from the origin is four units
and the line makes an angle of 120º with the positive direction of x-axis.
(A) 3x–y=0 (B) 3x+y=8 (C) x + 3y=8 (D) x – 3y=8

5. The point (–4,5) is the vertex of a square and one of its digonals is 7x–y+8 = 0. The equation
of the othere diagonals is
(A) 7x–y+23 = 0 (B) 7y + x =30 (C) 7y + x =31 (D) x –7y =30

6. The points A (1, 3) and C (5,1) are the oppositive vertices of rectangle. The equation of line

passing through other two vertices and of gradient 2, is

(A) 2x+y–8 = 0 (B) 2x–y– 4 = 0 (C) 2x–y+ 4 = 0 (D) 2x + y+4 = 0

7. Equation of a straight line passing through the origin and making with x  axis an angle twice
the size of the angle made by the line y = (0.2) x with the x  axis, is :
(A) y = (0.4) x (B) y = (5/12) x (C) 6y  5x = 0 (D) none of these

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-3
8. Equation of the line passing through the point (1, – 1) and perpendicular to the line 2x – 3y = 5
is -
(A) 3x + 2y – 1 = 0 (B) 2x + 3y + 1 = 0 (C) 3x + 2y – 3 = 0 (D) 3x + 2y + 5 = 0

9. If the line passing through the points (4, 3) and (2, ) is perpendicular to the line y = 2x + 3,
then  is equal to-
(A) 4 (B) – 4 (C) 1 (D) – 1

10. The equation of a line parallel to 2x – 3y = 4 which makes with the axes a triangle of area 12
units, is-
(A) 3x + 2y = 12 (B) 2x – 3y = 12 (C) 2x – 3y = 6 (D) 3x + 2y = 6

11. If the middle points of the sides BC, CA and AB of the triangle ABC be (1, 3), (5, 7) and
(– 5, 7) respectively then the equation of the side AB is
(A) x–y–2 = 0 (B) x–y+12 = 0 (C) x–y–12 = 0 (D) None of these

12. The distance of the point (2, 3) from the line 2 x  3 y + 9 = 0 measured along a line
x – y + 1 = 0 is :
(A) 5 3 (B) 4 2 (C) 3 2 (D) 2 2

13. From (1, 4) you travel 5 2 units by making 135° angle with positive x-axis (anticlockwise)
and then 4 units by making 120° angle with positive x-axis (clockwise) to reach Q. Find co-
ordinates of point Q.

(A) 6, 9  2 3  
(B) 6, 9  2 3  
(C) 6, 9  2 3  
(D) 6, 9  2 3 
14. A straight line is drawn through the point (2,3) and is inclined at an angle of 30º with the x-axis
. Find the coordinates of two points on it at a distance 4 from P.
(A) (2 +2 3 ,5) or (2 – 2 3 ,1) (B) (2 –2 3 , 5) or (2 – 2 3 ,1)
(C) (2 –2 3 ,5) or (2 + 2 3 ,1) (D) (2 +2 3 , 5) or (2 + 2 3 ,1)

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-4
 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 03
STRAIGHT LINE

TOPIC : CENTROID, INCENTRE , EXCENTRE

1. The quadrilateral formed by the points (a, –b), (0, 0), (–a, b) and (ab, – b2) is -
(A) rectangle (B) parallelogram (C) square (D) None of these

2. The points A(–4, –1), B (–2, –4), C (4, 0) and D(2, 3) are the vertices of
(A) square (B) rectangle (C) rhombus (D) None of these

3. If (3, – 4) and (–6, 5) are the extremities of the diagonal of a parallelogram and (–2, 1) is its
third vertex, then its fourth vertex is -
(A) (–1, 0) (B) (–1, 1) (C) (0, –1) (D) (0, 1)

4. The line bx + ay = 3ab cuts the coordinate axes at A and B, then centroid of OAB is -
(A) (b, a) (B) (a, b) (C) (a/3, b/3) (D) (3a, 3b)

5. The incentre of the triangle formed by (0, 0), (5, 12), (16, 12) is
(A) (7, 9) (B) (9, 7) (C) (–9, 7) (D) (–7, 9)

6. If two vertices joininig the hypotenuse of a right angled triangle are (0, 0) and (3, 4), then the
length of the median through the vertex having right angle is-
(A) 3 (B) 2 (C) 5/2 (D) 7/2

7. A variable straight line passes through a fixed point (a, b) intersecting the coordinates axes
at A & B. If 'O' is the origin, then the locus of the centroid of the triangle OAB is :
(A) bx + ay – 3xy = 0 (B) bx + ay – 2xy = 0
(C) ax + by – 3xy = 0 (D) ax + by – 2xy = 0

8. The sides of a triangle are the straight lines x + y = 1 ; 7y = x and 3 y + x = 0 . Then which
of the following is an interior point of the triangle ?
(A) circumcentre (B) centroid (C) incentre (D) orthocentre

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-5
9. The vertices of a triangle are (0, 0), (1, 0) and (0, 1). Then, ex-centre opposite to (0, 0) is :
 1 1   1 1 
(A)  1  ,1  (B)  1  ,1 
 2 2  2 2
 1 1   1 1 
(C)  1  ,1   (D)  1  ,1  
 2 2  2 2

10. Find the coordinates of incentre of the triangle whose vertices are (4, –2), (–2, 4) and (5, 5).
3 3 5 5
(A) (5, 5) (B)  ,  (C)  ,  (D) None of these
2 2 2 2

11. Given vertices A(1, 1), B(4, –2) & C(5, 5) of a triangle, find the equation of the perpendicular
dropped from C to the interior bisector of the angle A.
(A) y = 3 (B) x + y = 5 (C) y = 5 (D) x = 5

12. Column-I Column-II

(A) The lines y = 0; y = 1; x – 6y + 4 = 0 and x + 6y – 9 = 0 (P) a cyclic quadraliteral
constitute a figure which is
(B) The points A(a, 0), B(0, b), C(c, 0) and D(0, d) are (Q) a rhombus
such that ac = bd and a, b, c, d are all non-zero.
The points A, B, C and D always constitute
(C) The figure formed by the four lines (R) a square
ax ± by ± c = 0 (a  b), is
2 2
(D) The line pairs x – 8x + 12 = 0 and y – 14y + 45 = 0 (S) a trapezium
constitute a figure which is

2
13. The vertices of a triangle are (1, a), (2, b) and (c , –3)
(i) Prove that its centroid can not lie on the y-axis.
(ii) Find the condition that the centroid may lie on the x-axis.

14. If the coordinates of the mid point of the sides of a triangle are (1, 1), (2, –3) and (3, 4). Find
its (i) centroid (ii) incentre.

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-6
 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 04
STRAIGHT LINE

TOPIC : ORTHOCENTRE & CIRCUMCENTRE

1. Circumcentre of a triangle whose vertex are (0, 0), (4, 0) and (0, 6) is-
4 
(A)  , 2  (B) (0, 0) (C) (2, 3) (D) (4, 6)
3 

2. The orthocentre of the triangle ABC is 'B' and the circumcentre is S (a, b). If A is the origin,
then the coordinates of C are :
a b
(A) (2a, 2b) (B)  , 
2 2
(C)  a2  b2 , 0  (D) none

3. A triangle ABC with vertices A (– 1, 0), B (– 2, 3/4) & C (– 3, – 7/6) has its orthocentre H. Then
the orthocentre of triangle BCH will be :
(A) (– 3, – 2) (B) (1, 3) (C) (– 1, 2) (D) none of these

4. The circumcenter of the triangle formed by the line y = x, y = 2x, and y = 3x + 4 is

(A) (6, 8) (B) (6, –8) (C) (3, 4) (D) (–3, –4)

5. The vertices of a triangle are (6, 0), (0, 6) and (6, 6). Then distance between its circumcentre
and centroid, is
(A) 2 2 (B) 2 (C) 2 (D) 1

6. The vertices of a triangle are A(0, 0), B(0, 2) and C(2, 0).The distance between circumcentre
and orthocentre is :
1 1
(A) 2 (B) (C) 2 (D)
2 2

7. If the orthocentre and centroid of a triangle are (–3, 5) and (3, 3) then its circumcentre is :
(A) (6, 2) (B) (3, –1) (C) (–3, 5) (D) (–3, 1)

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-7
8. Column- Column-
(A) Two vertices of a triangle are (5, –1) and (–2, 3). (p) (–4, –7)
If orthocentre is the origin, then coordinates of the
third vertex are

(B) A point on the line x + y = 4 which lies at a unit (q) (–7, 11)
distance from the line 4x + 3y = 10, is

(C) Orthocentre of the triangle made by the lines (r) (1, –2)
x + y – 1 = 0, x – y + 3 = 0, 2x + y = 7 is :

(D) If a, b, c are in A.P., then liines ax + by = c (s) (–1, 2)

are concurrent at :
(t) (4, –7)

9. If (, ), (x, y) and (u, v) are respectively coordinates of the circumcentre, centroid and
orthocentre of a triangle, prove that 3 x = 2 + u and 3y = 2 + v

10. The vertices of a triangle are A(x1, x1 tan 1), B(x2, x2 tan 2), and C(x3, x3 tan 3). If the
circumcenter of ABC coincides with the origin and H(a, b) is the orthocenter, show that
a cos 1  cos 2  cos 3

b sin 1  sin 2  sin 3

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-8
 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 05
STRAIGHT LINE

TOPIC : LOCUS AND ITS EQUATION AND AREA OF TRIANGLE

1. Find the locus of a point which moves so that sum of the squares of its distance from the axes
is equal to 3.
2 2 2 2 2 2
(A) x + y = 9 (B) x +y + = 3 (C) |x|+|y|=3 (D) x – y = 3

2. AB is a variable line sliding between the co-ordinate axes in such a way that A lies on X-axis
and B lies on Y-axis. If P is a variable point on AB such that PA = b, PB = a and AB = a + b,
then equation of locus of P is
x2 y2 x2 y2 2 2 2 2
(A) 2
+ 2 =1 (B) 2
– 2 =1 (C) x + y = a + b (D) none of these
a b a b

3. The area of the triangle formed by the mid points of sides of the triangle whose vertices are
(2, 1), (– 2, 3), (4, – 3) is -
(A) 1.5 sq. units (B) 3 sq. units (C) 6 sq. units (D) 12 sq. units

4. The ends of the hypotenuse of a right angled triangle are (6, 0) and (0, 6), then find the locus
of third vertex of triangle.
(A) x2 + y2 + 12x – 12y = 0 (B) x2 + y2 – 6x – 6y = 0
2 2
(C) x – y + 6x + 6y = 0 (D) None of these

5. Find the locus of the centroid of a triangle whose vertices are (a cos t, a sin t),
(b sin t, –b cos t) and (1, 0), where ‘t’ is the parameter.
(A) (3x)2 + 9y2 = a2 + b2 (B) (3x – 1)2 + 9y2 = a2 + b2
2 2 2 2
(C) (3x + 1) + 9y = a + b (D) None of these

6. Find the area of the triangle formed by the mid points of sides of the triangle whose vertices
are (2, 1), (– 2, 3), (4, – 3)
(A) 1.5 sq. units (B) 3 sq. units (C) 6 sq. units (D) 12 sq. units

7. The locus of the mid-point of the distance between the axes of the variable line x cos  + y sin
 = p, where p is constant, is
2 2 2 1 1 4
(A) x + y = 4p (B) + 2
=
x 2
y p2
2 2 4 1 1 2
(C) x + y = 2
(D) – 2
=
p x 2
y p2

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-9
8. Find the locus of a point which moves so that sum of the squares of its distance from the axes
is equal to 3.
2 2 2 2 2 2
(A) x + y = 9 (B) x +y = 3 (C) |x|+|y|=3 (D) x – y = 3

9. A variable straight line passes through a fixed point (a, b) intersecting the coordinates axes
at A & B. If 'O' is the origin, then the locus of the centroid of the triangle OAB is :
(A) bx + ay  3xy = 0 (B) bx + ay  2xy = 0
(C) ax + by  3xy = 0 (D) ax + by  2xy = 0

10. Consider a triangle ABC, whose vertices are A(–2, 1), B(1, 3) and C(x, y). If C is a moving
point such that area of ABC is constant, then locus of C is :
(A) Straight line (B) Circle (C) Ray (D) Parabola

11. If the equation of the locus of a point equidistant from the points (a1, b1) and (a2, b2) is
(a1 – a2) x + (b1 – b2) y + c = 0, then the value of ‘c’ is :
1 2 2 2 2 2 2 2 2
(A) (a2 + b2 – a1 – b1 ) (B) a1 – a2 + b1 – b2
2
1 2 2 2 2
(C) (a1 + a2 + b1 + b2 ) (D) a12  b12  a22  b22
2

12. Two ends A & B of a straight line segment of constant length 'c' slide upon the fixed
rectangular axes OX & OY respectively. If the rectangle OAPB is completed. Then find locus
of the foot of the perpendicular drawn from P to AB.
2/3 2/3 2/3 2/3 2/3 1/3 1/3 1/3 2/3 1/3 1/3 1/3
(A) x + y = c (B) x + y = c (C) x + y = c (D) x + y = c

13. A and B are the points (3, 4) and (5, – 2) respectively. Find the co-ordinates of a point P such
that PA = PB and the area of the triangle PAB = 10.
(A) (7, 2) (B) (2, 7) (C) (1, 0) (D) (0, 1)

14. The line ‘1’ passing through the point (1, 1) and the ‘2’ passes through the point (– 1, 1). If
the difference of the slope of lines is 2. Find the locus of the point of intersection of the 1 and
2.
2 2 2 2
(A) x = y (B) y = 2 – x (C) y = x (D) x = 2 – y

Paragraph for question nos. 15 to 17

Consider a variable line L which passes through the point of intersection 'P' of the lines
3x + 4y – 12 = 0 and x + 2y – 5 = 0, meeting the coordinate axes at the points A and B.

15. Locus of the middle point of the segment AB has the equation
(A) 3x + 4y = 4xy (B) 3x + 4y = 3xy (C) 4x + 3y = 4xy (D) 4x + 3y = 3xy

16. Locus of the feet of the perpendicular from the origin on the variable line 'L' has the equation
2 2 2 2
(A) 2(x + y ) – 3x – 4y = 0 (B) 2(x + y ) – 4x – 3y = 0
2 2 2 2
(C) x + y – 2x – y = 0 (D) x + y – x – 2y = 0

17. Locus of the centroid of the variable triangle OAB has the equation (where 'O' is the origin)
(A) 3x + 4y + 6xy = 0 (B) 4x + 3y – 6xy = 0
(C) 3x + 4y – 6xy = 0 (D) 4x + 3y + 6xy = 0

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-10
18. Find the area of the quadrilateral with vertices as the points given in each of the following :
(i) (0, 0), (4, 3), (6, 0), (0, 3)
(ii) (0, 0), (a, 0), (a, b), (0, b)

19. The area of the triangle formed by the intersection of a line parallel to x-axis and passing
2
through P(h, k) with the lines y = x and x + y = 2 is 4h . Find the locus of the point P.

20. Show that equation of the locus of a point which moves so that difference of its distance from
x2 y2
two given points (ae, 0) and (–ae, 0) is equal to 2a is – = 1.
a2 a2 (e2  1)

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-11
 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 06
STRAIGHT LINE
TOPIC : TRANSFORMATION OF AXES POSITION OF TWO POINTS

1. At what point should the origin be shifted if the coordinates of a points (9, 5) become (– 3, 9)
(A) (–12,4) (B) (– 4, 7) (C) (7, – 4) (D) (12, – 4)

2. Find the new position of origin so that equation x2 +4x+8y –2 = 0 will not contain a term in x
and the costant term.
3  3   3  3
(A)  ,4  (B)  ,–2  (C)  2,  (D)  2,  
4  4   4   4 

3. Which pair of points lie on the same side of 3x – 8y – 7 = 0

(A) (0, –1) and (0, 0) (B) (4, –3) and (0, 1)
(C) (– 3, – 4) and (1, 2) (D) (–1, –1) and (3, 7)

4. The set of values of 'b' for which the origin and the point (1, 1) lie on the same side of the
straight line, a2x + a by + 1 = 0  a  R, b > 0 are :
(A) b  (2, 4) (B) b  (0, 2) (C) b  [0, 2] (D) (2, )

5. If the axes are rotated through an angle of 300 in the anticlockwise direction about the origin.
Find the coordinates of a point (4, – 2 3) in the new system w.r.t. the old system.
(A) (3 3,1) (B) (1,3 3 ) (C) (3 3, 1) (D) ( 1,3 3 )

6. What does the equation 2x2 + 4xy – 5y2 + 20x – 22y – 14 = 0 become when referred to the
rectangular axes through the point (–2, –3), the new axes being inclined at an angle of 45°
with the old axes ?
(A) x2 – 14xy – 7y2 – 2 = 0 (B) x2 + 14xy + 7y2 + 2 = 0
2 2
(C) x – 7xy – 7y – 2 = 0 (D) None of these

7. The equation 4xy – 3x2 = a2 become when the axes are turned through an angle tan–1 2 is :
(A) x2 + 4y2 = a2 (B) x2 – 4y2 = a2
2 2 2
(C) 4x + y = a (D) 4x2 – y2 = a2

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-12
8. Transform the equation x2 – 3xy + 11x – 12y + 36 = 0 to parallel axes through the point (–4, 1)
becomes ax2 + bxy + 1 = 0 then b2 – a =
1 1 1 1
(A) (B) (C) (D)
4 16 64 256

9. What does the equation (a – b)(x2 + y2) – 2abx = 0 become, if the origin be moved to the point
 ab 
 , 0 ?
 a  b 
(A) (a + b)2 (x + y)2 = a2b2 (B) (a2 – b2) (x2 + y2) = a2
(C) (a + b)2 (x + y)2 = a2 (D) (a – b)2 (x2 + y2) = a2b2

10. The equation x2 + 2xy + 4 = 0 transformed to the parallel axes through the point (6, ). For
what value of  its new form passes through the new origin ?
10 10 3 3
(A)  (B) (C) (D) 
3 3 10 10

11. Find the set of positive values of b for which the origin and the point (1, 1) lie on the same
side of the straigth line, a2x + a by + 1 = 0,  a  R.
(A) b  (–2, 2) (B) b  (0, 2) (C) b  (D) None of these

12. If the point (a, a) is placed in between the lines

|x + y| = 4, then find the values of a.
(A) |a| < 2 (B) |a| > 2 (C) a > 2 (D) |a| > 2

13. Determine all values of  for which the point (, 2) lies inside the triangle formed by the
lines 2x + 3y – 1 = 0, x + 2y – 3 = 0 and 5x – 6y – 1 = 0.
3  3   3  1 
(A)  ,   (B) (2, ) (C)  ,1  (2,  ) (D)   , 1   ,1
2  2   2  2 

14. Show that the area of the triangle with vertices (2,3) ; (5,7) and (–3,–1) remains invariant if the
origin is shifted to the point (–1, 3).

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-13
 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 07
STRAIGHT LINE
TOPIC : PERPENDICULAR DISTANCE, FOOT OF PERPENDICULAR.
IMAGE OF A POINT. DIST. B/W PARALLEL LINE & AREA OF PARALLELOGRAM

1. The figure formed by the lines 2x + 5y + 4 = 0, 5x + 2y + 7 = 0, 2x + 5y + 3 = 0 and

5x + 2y + 6 = 0 is
(A) Square (B) Rectangle (C) Rhombus (D) None of these

2. Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

|mn| 2 1 1
(A) (B) (C) (D)
(m  n)2 |mn| |mn| |mn|

3. The reflection of the point (4, –13) in the line 5x + y + 6 = 0 is

(A) (–1, –14) (B) (3, 4) (C) (1, 2) (D) (–4, 13)

4. The image of the point A (1, 2) by the line mirror y = x is the point B and the image of B by the
line mirror y = 0 is the point (, ), then :
(A)  = 1, =  2 (B)  = 0, = 0 (C)  = 2, =  1 (D) none of these

5. The foot of perpendicular drawn from point (1, 2) on the line L is (2, 3), then equation of line L
is
(A) x + y – 3 = 0 (B) x + y – 5 = 0 (C) x + y + 5 = 0 (D) 2x + y – 5 = 0

6. A light beam eminating from the point A(3, 10) reflects from the straight line 2x + y  6 = 0 and
then passes through the point B(4, 3). The equation of the reflected beam is :
(A) 3x  y + 1 = 0 (B) x + 3y  13 = 0 (C) 3x + y  15 = 0 (D) x  3y + 5 = 0

7. The nearest point on the line 3x + 4y – 1 = 0 from the origin is

 7 4   7 2   3 4   1 3 
(A)  ,  (B)  ,  (C)  ,  (D)  , 
 25 25   25 25   25 25   25 25 

8. Find coordinates of the foot of perpendicular, image and equation of perpendicular drawn from
the point (2, 3) to the line y = 3x – 4.

9. Starting at the origin, a beam of light hits a mirror (in the form of a line) at the point A(4, 8) and
reflected line passes through the point B (8, 12). Compute the slope of the mirror.

10. Prove that the area of the parallelogram contained by the lines 4y – 3x – a = 0,
2 2
3y – 4x + a = 0, 4y – 3x – 3a = 0 and 3y – 4x + 2a = 0 is a.
7
: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-14
 M AT HEM AT I CS

DPPDAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 08
STRAIGHT LINE
TOPIC : ANGLE BISECTOR, REFLECTION & REFRACTION OF LINES

1. The equation of bisectors of two lines L1 & L2 are 2 x  16 y  5 = 0 and 64 x + 8 y + 35 = 0. If

the line L1 passes through ( 11, 4), the equation of acute angle bisector of L1 & L2 is :
(A) 2 x  16 y  5 = 0 (B) 64 x + 8 y + 35 = 0
(C) 2x  16y  5 = 0 (D) 2x  16y  5 = 0

2. The equation of the internal bisector of BAC of ABC with vertices A(5, 2), B(2, 3) and
C(6, 5) is
(A) 2x + y + 12 = 0 (B) x + 2y – 12 = 0
(C) 2x + y – 12 = 0 (D) 2x – y – 12 = 0

3. The equation of the bisector of the angle between two lines 3 x  4 y + 12 = 0 and
12 x  5 y + 7 = 0 which contains the point (– 1, 4) is :
(A) 21x + 27y  121 = 0 (B) 21x  27y + 121 = 0
 3 x  4 y  12 12 x  5 y  7
(C) 21x + 27y + 191 = 0 (D) =
5 13

4. If the slope of one line of the pair of lines represented by ax2 + 10xy + y2 = 0 is four times the
slope of the other line, then a =
(A) 1 (B) 2 (C) 4 (D) 16

5. The combined equation of the bisectors of the angle between the lines represented by
(x2 + y2) 3 = 4xy is
x2  y2 xy
(A) y2 – x2 = 0 (B) xy = 0 (C) x2 + y2 = 2xy (D) =
3 2

6. A ray of light coming from the point (2,2, 3 ) is incident at an angle 30° on the line x = 1 at the
point A. The ray gets reflected on the line x = 1 and meets X-axis at the point B. then the line
AB passes through the point
 1   3
(A)  3,–  (B)  4,  
 3  2 


(C) 3,– 3  
(D) 4, – 3 

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-15
7. If L is the line whose equation is ax + by = c. Let M be the reflection of L through the y-axis,
and let N be the reflection of L through the x-axis. Which of the following must be true about M
and N for all choices of a, b and c?
(A) The x-intercepts of M and N are equal.
(B) The y-intercepts of M and N are equal.
(C) The slopes of M and N are equal.
(D) The slopes of M and N are reciprocal.

8. A ray of light along x + 3y= 3 get reflected upon reaching x-axis, the equation of the
reflected
ray is
(A) y = x + 3 (B) 3y=x– 3 (C) y = 3x– 3 (D) 3y=x–1

9. Find equations of acute and obtuse angle bisectors of the angle between the lines
4x + 3y – 7 = 0 and 24x + 7y – 31 = 0.

10. Find the equation of a straight line passing through the point (4, 5) and equally inclined to the
lines 3x = 4y + 7 and 5y = 12x + 6.

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-16
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 09
STRAIGHT LINE
TOPIC : FAMILY OF LINES AND CONDITION OF CONCURRENCY

1. The lines (p – q) x + (q – r) y + (r – p) = 0, (q – r) x + (r – p) y + (p – q) = 0
(r – p) x + (p – q) y + (q – r) = 0 are
(A) Parallel (B) perpendicular (C) Concurrent (D) None of these

2. The lines ax + by + c = 0, where 3a + 2b + 4c = 0, are concurrent at the point :

1 3 3 1
(A)  ,  (B) (1, 3) (C) (3, 1) (D)  , 
2 4 4 2

3. The equation of the line through the point of intersection of the lines y = 3 and x + y = 0 and
parallel to the line 2x – y = 4 is -
(A) 2x – y + 9 = 0 (B) 2x – y – 9 = 0 (C) 2x – y + 1 = 0 (D) None of these

4. The fix point through which the line x(a + 2b) + y(a + 3b) = a + b always passes for all values
of a and b, is-
(A) (2, 1) (B) (1, 2) (C) (2, –1) (D) (1, –2)

5. A straight line cuts intercepts from the coordinate axes sum of whose reciprocals is 1/p. It
passes through a fixed point -
(A) (1/ p, p) (B) (p, 1/p) (C) (1/p, 1/p) (D) (p, p)

6. The line parallel to the x-axis and passing through the intersection of the lines
ax + 2by + 3b = 0 and bx – 2ay –3a = 0, where (a, b) (0, 0) is
(A) Above the x-axis at a distance of 3/2 from it
(B) Above the x-axis at a distance of 2/3 from it
(C) Below the x-axis at a distance of 3/2 from it
(D) Below the x-axis at a distance of 2/3 from it

7. If a2 + 9b2  4c2 = 6ab, then the family of lines ax + by + c = 0 are concurrent at :

 1 3  1 –3   1 3  1 –3 
(A)  ,  – ,  (B)  – , –  – , 
 2 2  3 2   2 2  5 2 
 1 3  1 –3   1 3  1 3
(C)  – , –  – ,  (D)  – ,  , – 
 7 2  5 2   2 2  2 2
: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-17
8. The equation of a line passing through the point of intersection of the lines, x – 2y = 3 and
x + 3y = 8 having equal intercept on the co-ordinate axes is :
(A) x + y = 6 (B) x  5y = 0 (C) 5x  y = 0 (D) x + y = 5

9. The least positive value of t so that the lines x = t + a, y + 16 = 0 and y =ax are concurrent is

10. Consider the lines given by

L1 : x + 3y – 5 = 0
L2 : 3x – ky – 1 = 0
L3 : 5x + 2y – 12 = 0
Match the Statements/Expressions in Column I with the Statements / Expressions in Column
II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in
the ORS.
Column I Column II

(A) L1, L2, L3 are concurrent, if (p) k = –9

6
(B) One of L1, L2, L3 is parallel to at least one of the other two, if (q) k=–
5

5
(C) L1, L2, L3 form a triangle, if (r) k=
6

(D) L1, L2, L3 do not form a triangle, if (s) k=5

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-18
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 10
STRAIGHT LINE
TOPIC : PAIR OF ST.LINE & SEPRATION OF LINES & EQUATION OF ANGLE BISECTOR OF PSL & HOMOGENISATION

1. The equation 4x2 – 24xy + 11y2 = 0 represents

(A) x+y = 0 & x– 11 y = 0 (B) x–y = 0 & x+ 11 y = 0
(C) x–y = 0 & x– 11 y = 0 (D) x+y = 0 & x+ 11 y = 0

2. If the slope of one line of the pair of lines represented by ax2 + 10xy + y2 = 0 is four times the
slope of the other line, then 'a' equals to
(A) 1 (B) 2 (C) 4 (D) 16

3. The combined equation of the bisectors of the angle between the lines represented by
(x2 + y2) 3 = 4xy is
x2  y2 xy
(A) y2 – x2 = 0 (B) xy = 0 (C) x2 + y2 = 2xy (D) =
3 2

4. The equation of the lines represented by the equation ax2 + (a + b)xy + by2 + x + y = 0 are
(A) ax + by + 1 = 0, x + y = 0
(B) ax + by – 1 = 0, x + y = 0
(C) ax + by + 1 = 0
(D) None of these

5. The angle between the lines x2 – xy – 6y2 – 7x + 31y – 18 = 0 is

(A) 45° (B) 60° (C) 90° (D) 30°

6. If the equation 2x2 + k xy  3y2  x  4y  1 = 0 represents a pair of lines, then the value of 'k'
can be:
(A) 1, – 5 (B) 3, 5 (C)  1, 3 (D) 2, 5

7. If the equation 2x2 – 2xy – y2 – 6x + 6y + c = 0 represents a pair of lines, then ‘c’ is

(A) 2 (B) 3 (C) – 3 (D) 1

8. The straight lines joining the origin to the points of intersection of the line 2x + y = 1 and curve
3x2 + 4xy – 4x + 1 = 0 include an angle :
   
(A) (B) (C) (D)
2 3 4 6

9. If distance between the pair of parallel lines x2 + 2xy + y2 – 8ax – 8ay – 9a2 = 0 is 25 2 ,
then ‘a/5' is equal to
(A) ± 4 (B) ± 2 (C) ± 3 (D) ± 1
: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-19
10. If the distance between the lines represented 9x2 - 24xy + 16y2 + k(6x - 8y) = 0 is 4, then k
may be
(A) 3 (B) 10 (C) –10 (D) 7

11. If the straight lines joining the origin and the points of intersection of the curve
5x2 + 12xy  6y2 + 4x  2y + 3 = 0 and x + ky  1 = 0 are equally inclined to the x-axis, then
find the value of | k |.

12. If the points of intersection of curves C1 = 4 y2 – x2  2x y  9 x + 3 and

C2 = 2 x2 + 3 y2  4 x y + 3 x 1 subtends a right angle at origin, then find the value of .

13. The equation 9x3 + 9x2 y – 45x2 = 4y3 + 4xy2 – 20y2 represents 3 straight lines, two of which
passes through origin. Then find the area of the triangle formed by these lines

: 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
DOWNLOAD OUR APP & GET
UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-20
 ANSWER KEY
DPP-1
1. (D) 2. (C) 3. (C) 4. (B) 5. (A) 6. (B) 7. (A)
8. (A) 9. (C) 10. (B) 11. (B) 12. (C)
DPP-2
1. (B) 2. (B) 3. (B) 4. (B) 5. (C) 6. (B) 7. (B)
8. (A) 9. (A) 10. (B) 11. (B) 12. (B) 13. (B) 14. (A)

DPP-3
1. (D) 2. (B) 3. (A) 4. (B) 5. (A) 6. (C) 7. (A)
8. (BC) 9. (B) 10. (C) 11. (D) 12. (A) P, S; (B) P; (C) Q; (D) P, Q, R

DPP-4
1. (C) 2. (A) 3. (D) 4. (B) 5. (C) 6. (A) 7. (A)
8. (A)  p ; (B)  q ; (C)  s ; (D)  s
DPP-5
1. (B) 2. (A) 3. (A) 4. (B) 5. (B) 6. (A) 7. (B)
8. (B) 9. (A) 10. (A) 11. (A) 12. (A) 13. (A, C) 14. (A, B)
15. (A) 16. (B) 17. (C) 18. (i) 15 (ii) |ab|
19. y = 2x + 1 or y = –2x + 1
DPP-6
1. (D) 2. (C) 3. (D) 4. (B) 5. (C) 6. (A) 7. (B)
8. (C) 9. (D) 10. (A) 11. (B) 12. (A) 13. (D)

DPP-7
1. (C) 2. (D) 3. (A) 4. (C) 5. (B) 6. (B) 7. (C)

 23 29   13 14  1  10
8. Foot  10 , 10  , Image  5 , 5  , x + 3y – 11 = 0 9.
    3

DPP8
1. (A) 2. (C) 3. (A) 4. (D) 5. (A) 6. (C) 7. (C)
8. (B)
9. acute 2x + y – 3 = 0, obtuse x – 2y + 1 = 0, origin lies in obtuse angle bisector.
10. 9 x  7 y = 1, 7 x + 9 y = 73
DPP-9
1. (C) 2. (D) 3. (A) 4. (C) 5. (D) 6. (C) 7. (D)
8. (AB) 9. 8 10. (A) (s), (B) (p, q), (C) (r), (D) (p, q, s)

DPP-10

1. (C) 2. (D) 3. (A) 4. (A) 5. (A) 6. (A) 7. (B)

8. (A) 9. (D) 10. (BC) 11. 1 12. 19 13. 30

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE PAGE NO. 39

: www.atpstar.com
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 01
CIRCLE

TOPIC : BASICS OF CIRCLE

1. The length of the diameter of the circle x2 + y2 – 4x – 6y + 4 = 0 is -

(A) 9 (B) 3 (C) 4 (D) 6

2. Which of the following is the equation of a circle ?

(A) x2 + 2y2 – x + 6 = 0 (B) x2 – y2 + x + y + 1 = 0
(C) x2 + y2 + xy + 1 = 0 (D) 3(x2 + y2) + 5x + 1 = 0

3. The radius of the circle passing through the points (0, 0), (1, 0) and (0, 1) is-
(A) 2 (B) 1/ 2 (C) 2 (D) 1/2

4. If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2, y). Then the
value of x and y are-
(A) x = 1, y = 4 (B) x = 4, y = 1 (C) x = 8, y = 2 (D) None of these

5. If the equation px2 + (2 – q) xy + 3y2 – 6qx + 30 y + 6q = 0 represents a circle, then the values
of p and q are-
(A) 2, 2 (B) 3, 1 (C) 3, 2 (D) 3, 4

6. The centres of the circles x2 + y2 – 6x – 8y – 7 = 0 and x2 + y2 – 4x – 10y – 3 = 0 are the ends

of the diameter of the circle
(A) x2 + y2 – 5x – 9y + 26 = 0 (B) x2 + y2 + 5x – 9y + 14 = 0
(C) x2 + y2 + 5x – y – 14 = 0 (D) x2 + y2 + 5x + y + 14 = 0

7. The equation of the circle with centre on x-axis , radius 5 and passing through the point (2,3)
is
(A) x2 + y2 + 4 x – 21 = 0, x2 + y2 – 12x + 11 = 0
(B) x2 + y2 + 4 x + 21 = 0, x2 + y2 – 12x + 11 = 0
(C) x2 + y2 – 4 x – 21 = 0, x2 + y2 + 12x + 11 = 0
(D) x2 + y2 + 5 x – 21 = 0, x2 + y2 – 12x – 11 = 0

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-41

8. The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the xaxis in
points whose abscissa are roots of the equation:
(A) x² + ax + b = 0 (B) x²  ax + b = 0 (C) x² + ax  b = 0 (D) x²  ax  b = 0

9. The parametric equations of the circle 4x2 + 4y2 = 25 is

5 3 5 5
(A) x = cos  , y = sin  (B) x = cos  , y = sin 
2 2 2 2
7 7 1 1
(B) x = cos  , y = sin  (D) x = cos  , y = sin 
2 2 2 2

10. The line segment joining A (5, 0) and B (10 cos , 10 sin ) is divided internally in the ratio 2 :
3
at P. If  varies then the locus of P is
(A) (x + 3)2 + y2 = 16 (B) x2 + (y – 3)2 = 16
(C) (x – 3)2 + y2 = 16 (D) x2 + (y + 3)2 = 16

11. The locus of midpoints of the chords of the circle x2 – 2x + y2 – 2y + 1 = 0 which are of unit
length is
3
(A) (x – 1)2 + (y – 1)2 = (B) (x – 1)2 + (y – 1)2 = 2
4
1 2
(C) (x – 1)2 + (y – 1)2 = (D) (x – 1)2 + (y – 1)2 =
4 3


DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-42

 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 02
CIRCLE

TOPIC : EQUATION OF CIRCLE , POSITION OF A POINT

1. The circle x2 + y2 – 4x – 4y + 4 = 0
(A) touches x-axis only (B) touches both axes
(C) passes through the origin (D) touches y-axis only

2. The equation of the circle passing through the point (2,1) and touching y-axis at the origin is
(A) x2 + y2 – 5x = 0 (B) 2x2 + 2y2 – 5x = 0
(C) x2 + y2 + 5x = 0 (D) x2 – y2 – 5x = 0

3. A circle touches both the axes and its centre lies in the fourth quadrant. If its radius is 1 then
its equation will be -
(A) x2 + y2 – 2x + 2y + 1 = 0 (B) x2 + y2 + 2x – 2y – 1 = 0
(C) x2 + y2 – 2x – 2y + 1 = 0 (D) x2 + y2 + 2x – 2y + 1 = 0

4. The equation of a circle passing through (3, –6) and touching both the axes is
(A) x2 + y2 – 6x + 6y + 9 = 0 (B) x2 + y2 + 6x – 6y + 9 = 0
(C) x2 + y2 + 30x – 30y + 225 = 0 (D) x2 + y2 + 30x + 30y + 225 = 0

5. Equation of line passing through mid point of intercepts made by circle x2 + y2 – 4x – 6y = 0 on

co-ordinate axes is
(A) 3x + 2y – 12 = 0 (B) 3x + y – 6 = 0 (C) 3x + 4y – 12 = 0 (D) 3x + 2y – 6 = 0

6. The intercepts made by the circle x2 + y2 – 5x – 13y – 14 = 0 on the x-axis and y-axis are
respectively
(A) 9, 13 (B) 5, 13 (C) 9, 15 (D) none

7. The point (, 1 + ) lies inside the circle x2 + y2 = 1, then 

(A) (–1, 0) (B) (–2, 0) (C) (–3, 2) (D) (0, 2)

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-43

8. STATEMENT-1 : The length of intercept made by the circle x2 + y2 – 2x – 2y = 0 on the
x-axis is 2.
STATEMENT-2 : x2 + y2 – x – y = 0 is a circle which passes through origin with centre
   2  2
 ,  and radius
 2 2 2
(A) STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is correct explanation
for STATEMENT-1
(B) STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is not correct
explanation for STATEMENT-1
(C) STATEMENT-1 is true, STATEMENT-2 is false
(D) STATEMENT-1 is false, STATEMENT-2 is true

9. Equation of line passing through mid point of intercepts made by circle x2 + y2 – 4x – 6y = 0 on

co-ordinate axes is
(A) 3x + 2y – 12 = 0 (B) 3x + y – 6 = 0 (C) 3x + 4y – 12 = 0 (D) 3x + 2y – 6 = 0

10. If equation x2+ y2 + 2hxy + 2gx + 2fy + c = 0 represents a circle, then the condition for that
circle to pass through three quadrants only but not passing throuh the origin is
(A) f 2 > c (B) g2 > c (C) c > 0 (D) h = 0

11. Find equation of circle whose cartesian equation are x = –3 + 2 sin  , y = 4 + 2 cos 

12. Find the equation to the circle which touches the axis of x at a distance 3 from the origin and
intercepts a distance 6 on the axis of y.

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-44

 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 03
CIRCLE
TOPIC : LENGTH OF INTERCEPT & TANGENT OF A CIRCLE

1. The line 3x + 5y + 9 = 0 w.r.t. the circle x2 + y2 – 4x + 6y + 5 = 0 is

(A) chord (B) diameter (C) tangent (D) None

2. Find the co-ordinates of point on line x + y = – 13, nearest to the circle

x2 + y2 + 4x + 6y – 5 = 0
(A) (– 6, – 7) (B) (– 15, 2) (C) (– 5, – 6) (D) (– 7, – 6)

3. The coordinate of the point on the circle x² + y²  12x  4y + 30 = 0, which is farthest from the
origin are:
(A) (9, 3) (B) (8, 5) (C) (12, 4) (D) None

4. Radius of the circle with centre (3, –1) and cutting a chord of length 6 on the line
2x – 5y + 18 = 0 is
(A) 29 (B) 38 (C) 37 (D) 41

5. Line 3x + 4y = 25 touches the circle x2 + y2 = 25 at the point -

(A) (4, 3) (B) (3, 4) (C) (– 3, – 4) (D) None of these

6. The length of chord x + y – 1 = 0 w.r.t. circle x2 + y2 – 6x – 8y = 0 is

(A) 7 (B) 2 7 (C) 49 (D) 7

7. Find equation of tangent to the circle x2 + y2 – 30x + 6y + 109 = 0 at (4,–1)

(A) 11x + 2y – 46 = 0 (B) 11x – 2y – 46 = 0
(C) 11x + 2y + 46 = 0 (D) 11x – 3y – 46 = 0

8. The equation of a circle which touches both axes and the line 3x – 4y + 8 = 0 and whose
centre lies in the third quadrant is
(A) x2 + y2 – 4x + 4y – 4 = 0 (B) x2 + y2 – 4x + 4y + 4 = 0
(C) x2 + y2 + 4x + 4y + 4 = 0 (D) x2 + y2 – 4x – 4y – 4 = 0

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-45

9. The condition so that the line (x + g) cos + (y + f) sin  = k is a tangent to x2 + y2 + 2gx + 2fy
+ c = 0 is
(A) g2 + f2 = c + k2 (B) g2 + f2 = c2 + k (C) g2 + f2 = c2 + k2 (D) g2 + f2 = c + k

10. The tangent lines to the circle x² + y²  6x + 4y = 12 which are parallel to the line
4x + 3y + 5 = 0 are given by:
(A) 4x + 3y  7 = 0, 4x + 3y + 15 = 0 (B) 4x + 3y  31 = 0, 4x + 3y + 19 = 0
(C) 4x + 3y  17 = 0, 4x + 3y + 13 = 0 (D) none of these

11. The tangent to the circle x2 + y2 = 5 at the point (1, –2) also touches the circle
x2 + y2 – 8x + 6y + 20 = 0 at
(A) (–2, 1) (B) (–3, 0) (C) (–1, –1) (D) (3, –1)

12. Circle x2 + y2 – 4x – 8y – 5 = 0 will intersect the line 3x – 4y = m in two distinct points, if-
(A) – 10 < m < 5 (B) 9 < m < 20 (C) – 35 < m < 15 (D) None of these

13. Find the range of value of m for which the line y = mx + 2 cuts the circle x2 + y2 = 1 at distinct
or coincident points.

14. Find the greatest distance of the point P(10, 7) from the circle x2 + y2 – 4x – 10 = 0.

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-46

 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 04
CIRCLE
TOPIC : PAIR OF TANGENT, CHORD OF CONTACT, POWER TO A POINT,
DIRECTOR CIRCLE, NORMAL

1. The equation of the normal to the circle x2 + y2 = 2x, which is parallel to the line x + 2y = 3 is
(A) x + 3y = 7 (B) x + 2y = 1 (C) x + 2y = 2 (D) x + 2y = 5

2. The equation of normal to the circle x2 + y2 – 4x + 4y – 17 = 0 which passes through (1, 1) is

(A) 3x + y – 4 = 0 (B) x – y = 0 (C) x + y = 0 (D) None

3. The normal at the point (3, 4) on a circle cuts the circle at the point (–1, –2). Then the
equation of the circle is
(A) x2 + y2 + 2x – 2y – 13 = 0 (B*) x2 + y2 – 2x – 2y – 11 = 0
(C) x2 + y2 – 2x + 2y + 12 = 0 (D) x2 + y2 – 2x – 2y + 14 = 0

4. Statement-1: Angle between the tangents drawn from the point P(13, 6) to the circle
S : x2 + y2 – 6x + 8y – 75 = 0 is 90°.
because
Statement-2: Point P lies on the director circle of S.
(A)Statement-1 is true, statement-2 is true and statement-2 is correct explanation for
statement-1.
(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for
statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.

5. The number of tangents that can be drawn from the point (8, 6) to the circle x2 + y2 – 100 = 0
is
(A) 0 (B) 1 (C) 2 (D) None

6. A line segment through a point P cuts a given circle in 2 points A & B, such that PA = 16 & PB
= 9, then the length of tangent from point P to the circle is
(A) 7 (B) 25 (C) 12 (D) None of these

7. The equation of the tangents drawn from the origin to the circle x2 + y2 – 2rx – 2hy + h2 = 0 are
(A) x = 0, y = 0 (B) (h2 – r2) x–2rhy = 0, x = 0
(C) y = 0, x = 4 (D) (h2 – r2) x + 2rhy = 0, x = 0
DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-47

8. The length of the tangent drawn from the point (4, –1) to the circle 2x2 + 2y2 = 1 is
17 33 2
(A) (B) 33 (C) (D)
2 2

9. If the length of tangent drawn from the point (5, 3) to the circle x2 + y2 + 2x + ky + 17 = 0 is 7,
then k =
(A) – 6 (B) – 4 (C) 4 (D) 13/ 2

10. The length of the tangent drawn from any point on the circle x² + y² + 2gx + 2fy + p = 0 to the
circle x² + y² + 2gx + 2fy + q = 0 is:
(A) q  p (B) p  q (C) q  p (D) none

11. Two perpendicular tangents to the circle x2 + y2 = a2 meet at P. Then the locus of P has the
equation-
(A) x2 + y2 = 2a2 (B) x2 + y2 = 3a2 (C) x2 + y2 = 4a2 (D) None of these

12. The angle between the two tangents from the origin to the circle (x  7)² + (y + 1)² = 25 equal
  
(A) (B) (C) (D) None
4 3 2

13. The equation of the diameter of the circle (x – 2)2 + (y + 1)2 = 16 which bisects the chord cut
off by the circle on the line x – 2y – 3 = 0 is
(A) x + 2y = 0 (B) 2x + y – 3 = 0 (C) 3x + 2y – 4 = 0 (D) none

14. The co-ordinates of the middle point of the chord cut off on 2x – 5y + 18 = 0 by the circle
x2 + y2 – 6x + 2y – 54 = 0 are
(A) (1, 4) (B) (2, 4) (C) (4, 1) (D) (1, 1)

15. The distance between the chords of contact of tangents to the circle;
x² + y² + 2gx + 2fy + c = 0 from the origin & the point (g, f) is :
g2  f 2  c g2  f 2  c g2  f 2  c
(A) g2  f 2 (B) (C) (D)
2 2 g2  f 2 2 g2  f 2

16. The locus of the mid point of a chord of the circle x² + y² = 4 which subtends a right angle at
the origin is:
(A) x + y = 2 (B) x² + y² = 1 (C) x² + y² = 2 (D) x + y = 1

17. The locus of the mid points of the chords of the circle x² + y² + 4x  6y  12 = 0 which subtend

an angle of radians at its circumference is:
3
(A) (x  2)² + (y + 3)² = 6.25 (B) (x + 2)² + (y  3)² = 6.25
(C) (x + 2)² + (y  3)² = 18.75 (D) (x + 2)² + (y + 3)² = 18.75

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-48

18. If a circle of constant radius 3 2 passes through origin O and meets the coordinate axes at
A and B, then find the radius of director circle of locus of centroid of OAB.

Paragraph for question nos. 30003 & 30004

Let L1 : x – 2y = 3 and L2 : 2x + y = 11 be respectively tangent and normal to a circle with

centre 'C' and radius equal to 2 5 . Origin and centre 'C' lie on same side of the line L1.

19. If co-ordinates of C are (a, b), then (a + b) equals

(A) 4 (B) 6 (C) 8 (D) 9

20. If L3 is one more tangent to the given circle at angle of 45° with the line L1, then area of the
triangle formed by L1, L2 and L3 is
 
(A) 10 3  2 2 sq. units (B) 2 · 5  
2  1 sq. units

 
(C) 5 3  2 2 sq. units (D) 20  
2  1 sq. units

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-49

 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 05
CIRCLE

TOPIC : ANALYSIS OF TWO CIRCLES

1. Consider the circles x2 + (y – 1)2 = 9, (x – 1)2 + y2 = 25. They are such that-
(A) each of these circles lies outside the other
(B) one of these circles lies entirely inside the other
(C) these circles touch each other
(D) they intersect in two points

2. Number of common tangents of the circles (x + 2)²+(y2)² = 49 and (x  2)² + (y + 1)² = 4 is

(A) 0 (B) 1 (C) 2 (D) 3

3. The equation of the common tangent to the circle x2 + y2 – 4x – 6y – 12 = 0 and

x2 + y2 + 6x + 18y + 26 = 0 at their point of contact is
(A) 12x + 5y + 19 = 0 (B) 5x + 12y + 19 = 0
(C) 5x – 12y + 19 = 0 (D) 12x –5y + 19 = 0

4. Find the equations to the common tangents of the circles x2 + y2 – 2x – 6y + 9 = 0 and

x2 + y2 + 6x – 2y + 1 = 0
(A) x = 0, 3x + 4y = 10, y = 4, 3y = 4x. (B) x = 0, 3x – 4y = 10, y = 4, 3y = 4x.
(C) x = 0, 3x + 4y = 10, y = 4, 3y + 4x = 0 (D) x = 0, 3x – 4y = 10, y = 4, 3y – 4x = 0

5. Find the length of direct common tangent of circle(x – 1)2 + (y – 2)2 = 4 and (x – 5)2+(y –2)2= 1
(A) 14 (B) 15 (C) 5 (D) 7

6. If the length of a common internal tangent to two circles is 7, and that of a common external
tangent is 11, then the product of the radii of the two circles is:
(A) 18 (B) 20 (C) 16 (D) 12

7. If the two circles, x2 + y2 + 2 g1x + 2 f1y = 0 & x2 + y2 + 2 g2x + 2 f2y = 0 touch each other then:
f1 f
(A) f1 g1 = f2 g2 (B) = 2 (C) f1 f2 = g1 g2 (D) none
g1 g2
8. If the length of a common internal tangent to two circles is 7, and that of a common external
tangent is 11, then the product of the radii of the two circles is:
(A) 36 (B) 9 (C) 18 (D) 4

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-50

9. The equation(s) to the common tangents of the circles x2 + y2 – 2x – 6y + 9 = 0 and
x2 + y2 + 6x – 2y + 1 = 0 is
(A) x = 0, y = 4 (B) 3x + 4y = 10 (C) 3y = 4x (D) all of these

10. For the circles x2 + y2 – 10x + 16y + 89 – r2 = 0 and x2 + y2 + 6x – 14y + 42 = 0 which of the
following
is/are true.
(A) Number of integral values of r are 14 for which circles are intersecting.
(B) Number of integral values of r are 9 for which circles are intersecting.
(C) For r equal to 13 number of common tangents are 3.
(D) For r equal to 21 number of common tangents are 2.

11. Two circles, each of radius 5 units, touch each other at (1, 2). If the equation of their common
tangent is 4x + 3y = 10. The equations of the circles are
(A) x² + y² + 6x + 2y  15 = 0 (B) x² + y²  10x  10y + 25 = 0
(C) x² + y² – 6x + 2y  15 = 0 (D) x² + y²  10x  10y + 25 = 0

12. Column - I Column - II

(A) Number of common tangents of the circles (p) 0
x2 + y2 – 2x = 0 and x2 + y2 + 6x – 6y + 2 = 0 is
(B) Number of indirect common tangents of the circles (q) 1
x2 + y2 – 4x – 10y + 4 = 0 & x2 + y2 – 6x – 12y – 55 = 0 is
(C) Number of common tangents of the circles (r) 2
x2 + y2 – 2x – 4y = 0 & x2 + y2 – 8y – 4 = 0 is
(D) Number of direct common tangents of the circles (s) 3
x2 + y2 + 2x – 8y + 13 = 0 & x2 + y2 – 6x – 2y + 6 = 0 is

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-51

 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 06
CIRCLE
TOPIC : COMMON CHORD & ANGLE BETWEEN TWO CIRCLES
ORTHOGONAL CIRCLES

1. The locus of the centre of the circle which bisects the circumferences of the circles
x² + y² = 4 & x² + y²  2x + 6y + 1 = 0 is:
(A) a straight line (B) a circle (C) a parabola (D) none of these

2. Two circles whose radii are equal to 4 and 8 intersect at right angles. The length of their
common chord is:
16 8 5
(A) (B) 8 (C) 4 6 (D)
5 5

3. If the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2 + 2ky + k = 0 intersect orthogonally, then k

is
3 3 3 3
(A) 2 or – (B) – 2 or – (C) 2 or (D) – 2 or
2 2 2 2

4. Equation of the circle cutting orthogonally the three circles x2 + y2 – 2x + 3y – 7 = 0,

x2 + y2 + 5x – 5y + 9 = 0 and x2 + y2 + 7x – 9y + 29 = 0 is
(A) x2 + y2 – 16x – 18y – 4 = 0 (B) x2 + y2 – 7x + 11y + 6 = 0
(C) x2 + y2 + 2x – 8y + 9 = 0 (D) None of these

5. The equation of the circle which passes through the origin has its centre on the line x + y = 4
and cuts the circle x2 + y2 – 4x + 2y + 4 = 0 orthogonally, is-
(A) x2 + y2 – 2x – 6y = 0 (B) x2 + y2 – 6x – 3y = 0
(C) x2 + y2 – 4x – 4y = 0 (D) None of these

6. The angle of intersection of two circles is 0º if -

(A) they are separate (B) they intersect at two points
(C) they intersect only at a single point (D) it is not possible

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-52

7. If the circle C1: x² + y² = 16 intersects another circle C2 of radius 5 in such a manner that the
common chord is of maximum length and has a slope equal to 3/4, then the coordinates of
the centre of C2 are:
 9 12   9 12   12 9  12 9
(A)   ,   (B)   ,   (C)   ,   (D)   ,  
 5 5   5 5   5 5  5 5

8. If the circle C1: x² + y² = 16 intersects another circle C2 of radius 5 in such a manner that the
common chord is of maximum length and has a slope equal to 3/4, then the coordinates of
the centre of C2 are:
 9 12  9 12   9 12   9 12 
(A)  ,  (B)  ,  (C)  ,  (D)  , 
 5 5  5 5   5 5   5 5 

9. Which of the following statement(s) is/are correct with respect to the circles
S1  x2 + y2 – 4 = 0 and S2  x2 + y2 – 2x – 4y + 4 = 0 ?
(A) S1 and S2 intersect at an angle of 90°.
6 8
(B) The point of intersection of the two circle are (2, 0) and  ,  .
5 5
4
(C) Length of the common of chord of S1 and S2 is .
5
(D) The point (2, 3) lies outside the circles S1 and S2.

10. Two circles whose radii are equal to 4 and 8 intersect at right angles. The length of their

common chord is , then find 
5

11. Column-I Column-I

(A) The length of the common chord of two circles
of radii 3 and 4 units which intersect orthogonally is (p) 1
k
, then k equals to
5
(B) The circumference of the circle x2 +y2 + 4x + 12y + p = 0 is (q) 24
bisected by the circlc x2 + y2 –2x + 8y – q = 0, then
p + q is equal to
(C) Number of distinct chords of the circles (r) 32
2x(x– 2 ) + y (2y – 1) = 0 is passing through the point
 1
 2,  and are bisected by x-axis is
 2
(D) One of the diameters of the circles circumscribing the (s) 36
rectangle ABCD is 4y = x + 7. If A and B are the points
(–3,4) and (5,4) respectively, then the area of the
rectangle is equal to

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-53

 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 07
CIRCLE
TOPIC : FAMILY OF CIRCLE, RADICAL AXIS & RADICAL CENTRE

1. The locus of the centre of the circle which bisects the circumferences of the circles
x² + y² = 4 & x² + y²  2x + 6y + 1 = 0 is:
(A) a straight line (B) a circle (C) a parabola (D) none of these

2. The circle x² + y² = 4 cuts the circle x² + y² + 2x + 3y  5 = 0 in A & B. Then the equation of the
circle on AB as a diameter is:
(A) 13(x² + y²)  4x  6y  50 = 0 (B) 9(x² + y²) + 8x  4y + 25 = 0
(C) x² + y²  5x + 2y + 72 = 0 (D) None of these

3. Find equation of circle passing through the point (4,4) and touching the line x + y –2 = 0 at
(1,1)
(A) x2 + y2 – 5x + 5y + 8 = 0 (B) x2 + y2 – 5x – 5y + 8 = 0
(C) x2 + y2 + 5x – 5y + 8 = 0 (D) x2 + y2 – 5x – 5y – 8 = 0

4. Find equation of circle passing through the points (1,1) and (3,3) and whose centre lies an x-
axis
(A) x2 + y2 + 8x + 6 = 0 (B) x2 + y2 – 8x – 6 = 0
(C) x2 + y2 – 8x + 6 = 0 (D) x2 + y2 – 8x – 8 = 0

5. Equation of a circle drawn on the chord x cos  + y sin  = p of the circle x2 + y2 = a2 as its
diameter, is
(A) (x2 + y2 – a2) –2p (xsin + ycos – p) = 0
(B) (x2 + y2 – a2) –2p (xcos + ysin – p) = 0
(C) (x2 + y2 – a2) + 2p (xcos + ysin – p) = 0
(D) (x2 + y2 – a2) –p (xcos + ysin – p) = 0

6. Find the equation of the circle which passes through the point (1, 1) & which touches the circle
x² + y² + 4x  6y  3 = 0 at the point (2, 3) on it.
(A) x² + y² + x  6y + 3 = 0 (B) x² + y² + x  6y – 3 = 0
(C) x² + y² + x  6y + 3 = 0 (D) x² + y² + x  3y + 3 = 0

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-54

7. Find the equation of circle touching the line 2x + 3y + 1 = 0 at (1, – 1) and cutting orthogonally
the circle having line segment joining (0, 3) and (– 2, – 1) as diameter.
(A) 2x2 + 2y2 – 10x– 5y + 1 = 0 (B) 2x2 + 2y2 – 10x+ 5y + 1 = 0
2 2
(C) 2x + 2y – 10x– 5y – 1 = 0 (D) 2x2 + 2y2 + 10x– 5y + 1 = 0

8. Equation of the circle which passes through the point (–1, 2) & touches the circle
x2 + y2 – 8x + 6y = 0 at origin, is -
3
(A) x2 + y2 – 2x – y = 0 (B) x2 + y2 + x – 2y = 0
2
3 3
(C) x2 + y2 + 2x + y = 0 (D) x2 + y2 + 2x – y = 0
2 2

9. Two circles are drawn through the point (a, 5a) and (4a, a) to touch the axis of ‘y’. They
intersect at an angle of  then tan is -
40 9 1 1
(A) (B) (C) (D)
9 40 9 3

10. The circle x2 + y2  2 x  3 k y  2 = 0 passes through two fixed points, (k is the parameter)

(A) 1  3, 0  
(B)  1  3, 0  
(C)  3  1, 0  
(D) 1  3, 0 
11. The equation of a circle passing through points of intersection of the circles
x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0 and point (1,1) is

12. Consider a family of circles passing through two fixed points A (3, 7) and B (6, 5). Show that
the chords in which the circles x2 + y2 – 4x – 3 = 0 cuts the members of the family are
concurrent at a point. Also find the co-ordinates of this point.

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-55

 ANSWER KEY
DPP-1

1. (D) 2. (D) 3. (B) 4. (A) 5. (C) 6. (A) 7. (A)

8. (B) 9. (B) 10. (C) 11. (A)

DPP-2

1. (B) 2. (B) 3. (A) 4. (A) 5. (D) 6. (C) 7. (A)

8. (C) 9. (D) 10. (ABCD)

11. (x + 3)2 + (y – 4)2 = 4 12. x2 + y2 ± 6 2y ± 6x + 9 = 0

DPP-3
1. (B) 2. (A) 3. (A) 4. (B) 5. (B) 6. (B) 7. (B)

8. (C) 9. (A) 10. (B) 11. (D) 12. (C) 13. m2  3

14. 113  14

DPP-4
1. (B) 2. (A) 3. (B) 4. (A) 5. (B) 6. (C) 7. (B)

8. (C) 9. (B) 10. (A) 11. (A) 12. (C) 13. (B) 14. (A)

15. (C) 16. (C) 17. (B) 18. (4) 19. (C) 20. (A)

DPP-5
1. (B) 2. (B) 3. (B) 4. (A) 5. (B) 6. (A) 7. (B)

8. (C) 9. (D) 10. (A,C) 11. (A,B)

12. (A)  s; (B)  p; (C)  q; (D)  r

DPP-6
1. (A) 2. (A) 3. (B) 4. (C) 5. (B) 6. (A) 7. (A)

 52 23 
8. (D) 9. (A) 10. (A, D) 11. 4x2 + 4y2 + 30x – 13y – 25 = 0 12.  , – 
 3 9 

DPP-6
1. (A) 2. (A) 3. (A) 4. (A) 5. (C) 6. (C) 7. (B)
8. (B) 9. (ACD) 10. (16) 11. Aq;Bs; Cp;Dr

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE PAGE NO. 72

: www.atpstar.com
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 01
PARABOLA
TOPIC : BASIC OF CONIC SECTION AND BASIC OF PARABOLA

1. For what value of  the equation of conic

2xy + 4x – 6y +  = 0 represents two intersecting straight lines ?
(A) –12 (B) 12 (C) 17 (D) –17

2. The equation of the conic with focus at (1,–1), directrix along x – y + 1 = 0 and with
eccentricity 2 is :
(A) x2 – y2 = 1 (B) xy = 1
(C) 2xy – 4x + 4y + 1 = 0 (D) 2xy – 4x – 4y – 1 = 0

3. The equation (x2 – a2) – y4 = 0 represents :

(A) A circle (B) four straight lines
(C) a hyperbola (D) a parabola

4. The equation of the parabola whose focus is ( 3, 0) and the directrix is, x + 5 = 0 is:
(A) y2 = 4 (x  4) (B) y2 = 2 (x + 4) (C) y2 = 4 (x  3) (D) y2 = 4 (x + 4)

5. If (2, 0) is the vertex & y  axis is the directrix of a parabola, then its focus is:
(A) (2, 0) (B) ( 2, 0) (C) (4, 0) (D) ( 4, 0)

6. Length of the latus rectum of the parabola 25 [(x  2)2 + (y  3)2] = (3x  4y + 7)2 is:
(A) 4 (B) 2 (C) 1/5 (D) 2/5

7. The point on the parabola y2 = 12x whose focal distance is 4, are

  
(A) 2, 3 , 2,  3   
(B) 1, 2 3 , 1,  2 3 
(C) (1, 2) (D) none of these

8. The latus rectum of a parabola whose directrix is x + y – 2 = 0 and focus is (3, – 4), is
(A) –3 2 (B) 3 2 (C) 2 2 (D) 3/ 2

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-74

9. A parabola is drawn with its focus at (3, 4) and vertex at the focus of the parabola y2  12 x  4
y + 4 =0. The equation of the parabola is:
(A) x2  6 x  8 y + 25 = 0 (B) y2  8 x  6 y + 25 = 0
(C) x2  6 x + 8 y  25 = 0 (D) x2 + 6 x  8 y  25 = 0

10. The length of the side of an equilateral triangle inscribed in the parabola, y2 = 4x so that one
of its angular point is at the vertex is:
(A) 8 3 (B) 6 3 (C) 4 3 (D) 2 3

11. The ends of latus rectum of parabola x2 + 8y = 0 are

(A) (–4, –2) and (4, 2) (B) (4, 2) and (–4, 2)
(C) (–4, –2) and (4, –2) (D) (4, 2) and (4, –2)

12. The equation of the latus rectum of the parabola x2 + 4x + 2y = 0 is

(A) 2y + 3 = 0 (B) 3y = 2 (C) 2y = 3 (D) 3y = – 2

13. The focal distance of a point on the parabola y2 = 16 x whose ordinate is twice the abscissa, is
(A) 6 (B) 8 (C) 10 (D) 12

14. Which one of the following equations parametrically represents equation to a parabolic
profile?
t
(A) x = 3 cos t; y = 4 sin t (B) x2  2 =  2 cos t; y = 4 cos2
2
x = tan t; t t
(C) y = sec t (D) x = 1  sint ; y = sin + cos
2 2

15. The latus rectum of a parabola whose focal chord is PSQ such that SP = 3 and SQ = 2 is
given by:
(A) 24/5 (B) 12/5 (C) 6/5 (D) none of these

16. The locus of the mid point of the focal radii of a variable point P moving on the parabola y2 =
8x, is a parabola whose latus rectum is
(A) 1 (B) 2 (C) 3 (D) 4

17. Let 'L' be the point (t, 2) and 'M ' be a point on the y-axis such that 'LM' has slope –t,
then the locus of the midpoint of 'LM' , as t varies over real values, is a parabola, whose
(A) vertex is (0, 2) (B) lengths of latus-rectum is 2
 17 
(C) focus is  0, (D) equation of directrix is 8y – 15 = 0
 8 

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-75

 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 02
PARABOLA
TOPIC : FOCAL CHORD

2
1. The locus of the middle points of the focal chords of the parabola, y = 4x is:
2 2 2 2
(A) y = x  1 (B) y = 2 (x  1) (C) y = 2 (1  x) (D) y = 2(x + 1)

2. The length of chord intercepted on the line 2x + y = 2 by the parabola y2 = 4x, is

(A) 5 (B) 3 (C) 2 (D) 1

3. A variable chord PQ of the parabola, y2 = 4x is drawn parallel to the line y = x. If the

parameters of the points P & Q on the parabola be p & q respectively, then (p + q) equal to.
(A) 1 (B) 1/2 (C) 2 (D) 4

4. The length of the chord of the parabola, y2 = 12x passing through the vertex & making an
angle of 60º with the axis of x is:
(A) 8 (B) 4 (C) 16/3 (D) none of these

5. If one end of a focal chord of the parabola y2 = 4x is (1, 2), the other end lies on
(A) x2 y + 2 = 0 (B) xy + 2 = 0 (C) xy – 2 = 0 (D) x2 + xy – y – 1 = 0

6. If one end of a focal chord of the parabola y2 = 4x is (1, 2), the other end is
(A) (1, – 2) (B) (2, 2) (C) (2, 1) (D) (–2, –1)

7. In the parabola y2 = 6x, the equation of the chord through vertex and negative end of latus
rectum, is
(A) y = 2x (B) y + 2x = 0 (C) y + 3x = 0 (D) x + 2y = 0

8. Length of the focal chord of the parabola y2 = 4ax at a distance p from the vertex is:
2a2 a3 4a3 p2
(A) (B) (C) (D)
p p2 p2 a
9. If the segment intercepted by the parabola y2 = 4ax with the line x + my + n = 0 subtends a
right angle at the vertex, then
(A) 4a+ n = 0 (B) 4a+ 4am + n = 0
(C) 4am + n = 0 (D) None of these

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-76

10. The locus of the mid point of the focal radii of a variable point moving on the parabola,
y2 = 4ax is a parabola whose
(A) Latus rectum is half the latus rectum of the original parabola
(B) Vertex is (a/2, 0)
(C) Directrix is y-axis
(D) All of these

Comprehension (Q.11 to Q.13 )

2
Let PQ be a variable focal chord of the parabola y = 4ax where vertex is A. Locus of, centroid
of triangle APQ is a parabola ‘P1’

11. Latus rectum of parabola P1 is

2a 4a 8a 16a
(A) (B) (C) (D)
3 3 3 3

12. Vertex of parabola P1 is

 2a   4a   8a  a 
(A)  , 0  (B)  , 0  (C)  , 0  (D)  , 0 
 3   3   3  3 

13. Let 1 is the area of triangle formed by joining points T1, T2 and T3 on parabola P1 and 2 be
the area of triangle T formed by tangents at T1, T2 and T3, then
(A) 2 = 21
(B) 1 = 42
(C) orthocentre of triangle T lies on x = a/3.
(D) Both (A) and (C) are correct.

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-77

 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 03
PARABOLA
TOPIC : TANGENT OF PARABOLA & PROPERTIES OF TANGENTS

1. Point (2,3) lies

(A) In side the parabola y2 = 4x (B) In side the parabola x2 = 4y
(C) On the parabola y2 = 4x (D) On the parabola x2 = 4y

2. If the point (– 1,) lies in side the parabola x2 = 4(y–1) then range of values of  is
(A) (1, 5) (B) (4, 7) (C) (2, 9) (D) (0, 4)

3. The value  such that line y = x +  is tangent to the parabola y2 = 8x

(A) 2 (B) 4 (C) 6 (D) 8

 1
4. If y = 2 x  3 is a tangent to the parabola y2 = 4a  x   , then ' a ' is equal to:
 3
14  14
(A) 1 (B)  1 (C) (D)
3 3

5. The equation of the tangent to the parabola y = (x  3)2 parallel to the chord joining the points
(3, 0) and (4, 1) is:
(A) 2 x  2 y + 6 = 0 (B) 2 y  2 x + 6 = 0 (C) 4 y  4 x + 11 = 0 (D) 4 x  4 y = 13

y
6. The value of a such that line = x –1 is tangent to the parabola y2=6x, parallel to the line
a3 a
x+ y= 4.
3
(A) – 4 (B) – 3 (C) – (D) – 2
2

7. The tangent drawn at any point P to the parabola y2 = 4ax meets the directrix at the point K,
then angle which KP subtends at its focus is
(A) 30º (B) 45º (C) 60º (D) 90º

8. Equation of a tangent to the parabola y2 = 12x which make an angle of 45° with line
y = 3x + 77 is
(A) 2x – 4y + 3 = 0 (B) x + 2y + 12 = 0 (C) 4x + 2y + 3 = 0 (D) 2x + y – 12 = 0

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-78

9. The mirror image of the parabola y2 = 4x in the tangent to the parabola at the point (1, 2) is
(A) (x – 1)2 = 4(y – 2) (B) (x + 3)2 = 4(y + 2)
(C) (x + 1)2 = 4(y – 1) (D) (x – 1)2 = 4 (y – 1)

10. The equation of tangent to the parabola y2 = 9x, which pass through the point (4, 10) is
(A) 4y = 9x + 4 (B) 4y = x – 36 (C) y = x + 36 (D) 4y = x + 32

11. Let y2 = 4ax be a parabola and x2 + y2 + 2 bx = 0 be a circle. If parabola and circle touch each
other externally then:
(A) a > 0, b > 0 (B) a > 0, b < 0 (C) a < 0, b > 0 (D) ab > 0

12. The circles on focal radii of a parabola as diameter touch:

(A) the tangent at the vertex (B) the axis
(C) the directrix (D) none of these

13. If T (3, 2) is the foot of perpendicular drawn from focus S(2, –1) on a tangent and directrix
passes through P(0, 9), then
(A) length of latus rectum of parabola is 8 2 .
(B) equation of tangent at vertex is x + y – 5 = 0.
(C) equation of axis of parabola is x – y = 3.
(D) directrix is at a distance 2 2 from focus.

14. TP and TQ are tangents to parabola y2 = 4x at P and Q, where T is any point on

y2 = 4(x + 1). If the locus of the middle point of chord PQ is a parabola whose length of latus
rectum is L, then find the value of (50) L.

Paragraph for Question no. 15 to 17

Let two distinct tangents are drawn from a point (p, p + 1) on the line y = x + 1 to the curve
y = 2x2. Also k is the least positive integral value of p.

15. The value of k is

(A) 1 (B) 2 (C) 5 (D) 9

16. Sum of slopes of two tangents drawn from the point (k, k + 3) to the curve y = 2x2, is
(A) 8 (B) 10 (C) 12 (D) 16

 k 
17. If focal chord of the curve y = 2x2 passes through the point  8k, then the length of this
 16 
chord, is
1 1 1
(A) (B) (C) (D) 1
8 4 2

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-79

 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 04
PARABOLA
TOPIC : NORMAL TO PARABOLA & CO-NORMAL POINTS

1. Equation of the normal to the parabola, y2 = 4ax at its point (am2, 2am) is:
(A) y =  mx + 2am + am3 (B) y = mx  2am  am3
3
(C) y = mx + 2am + am (D) none

2. At what point on the parabola y2 = 4x the normal makes equal angles with the axes?
(A) (4, 4) (B) (9, 6) (C) (4, – 1) (D) (1, 2)

3. The line 2x + y +  = 0 is a normal to the parabola y2 = – 8x, then  is

(A) 12 (B) – 12 (C) 24 (D) – 24

4. The distance between a tangent to the parabola y2 = 4 A x (A > 0) and the parallel normal with
gradient 1 is :
(A) 4 A (B) 2 2 A (C) 2 A (D) 2A

5. If a line x + y = 1 cut the parabola y2 = 4ax in points A and B and normals drawn at A and B
meet at C. The normal to the parabola from C other, than above two meet the parabola in D,
then point D is
(A) (a, a,) (B) (2a, 2a) (C) (3a, 3a) (D) (4a, 4a)

6. Number of distinct normals of a parabola passing through the focus of the parabola is
(A) 0 (B) 1 (C) 2 (D) 3

7. Length of common chord of the parabolas x2 = 4y and y2 = 4x is

(A) 4 (B) 4 3 (C) 4 2 (D) 2

8. The circle x2 + y2 = 5 meets the parabola y2 = 4x at P & Q. Then the length PQ is equal to
(A) 1 (B) 2 (C) 3 (D) 4

9. PQ is a double ordinate of the parabola y2 = 8x. If the normal at P intersect the line passing
through Q and parallel to axis of x at G, then the locus of G is a parabola with
(A) vertex at (8, 0) (B) focus at (10, 0)
(C) length of latus rectum equals 8 (D) equation of directrix is x = 6.

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-80

10. PQ and RS are normal chord to parabola y2 = 8x at P & R on the curve respectively and
the points P, Q, R, S are concyclic. If A is vertex of parabola, then
(A) centroid of APR lies on x-axis
(B) centroid of APR lies on y-axis
(C) PR is parallel to tangent at the vertex
(D) PR is parallel to axis of parabola

11. From point P(6, 0) three normals are drawn to the parabola y2 = 8x and points A, B and C
are co-normal points. Then which of the following is/are correct?
(A) Area of ABC is 8 (B) Circum-centre of ABC is (5, 0)
4 
(C) Centroid of ABC is  ,0  (D) ABC is a right angled triangle
3 

12. If normal chord of the parabola 2y2 = x is inclined at an angle 15º with the axis of the
parabola. Then find the area of the triangle formed by the normal chord of the parabola and
the tangents drawn at extremities of the normal chord.

Paragraph for question nos. 13 to 15

Let AB be variable chord of the parabola P : y2 = 4ax such that the normals at A and B
intersect at the point C (at2, 2at).

13. Centroid of the triangle ABC has the coordinates

 2a  a   2a  a 
(A)  (t 2  2), 0  (B)  (t 2  2), 0  (C)  (2  t 2 ), 0  (D)  (2  t 2 ), 0 
 3  3   3  3 

14. AB passes through a fixed point whose coordinates are

(A) (– a, 0) (B) (2a, 0) (C) (–2a, 0) (D) (a, 0)

15. The circle circumscribing the triangle ABC always passes through
(A) focus of P (B) vertex of P
(C) foot of the directrix of P (D) (2a, 0)

16. STATEMENT-1 : Normal chord drawn at the point (8, 8) of the parabola y2 = 8x subtends a
right angle at the vertex of the parabola.
STATEMENT-2 : Every chord of the parabola y2 = 4ax passing through the point (4a, 0)
subtends a right angle at the vertex of the parabola.

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-81

 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 05
PARABOLA
TOPIC : PAIR OF TANGENT, CHORD OF CONTACT, DIAMETER

1. The line 4x  7y + 10 = 0 intersects the parabola, y2 = 4x at the points A & B. The co-ordinates
of the point of intersection of the tangents drawn at the points A & B are:
7 5  5 7 5 7  7 5
(A)  ,  (B)   ,   (C)  ,  (D)   ,  
2 2 2 2   2 2 2 2 

2. The equation of director circle of the parabola y2 = 10(x – 1)

(A) x2 + y2 –2x –4 y + 4 = 0
(B) 2x + 3 = 0
(C) 2x + 5 = 0
(D) x2 + y2 – 4x + 2y + 2 = 0

3. The equation of tangent drawn from the point (2,3) to the parabola y2 = 4x,are
(A) x–y+1 = 0, x+2y = 4 (B) x+y–1= 0, x+2y +4 = 0
(C) x–y+1= 0, x–2y +4 = 0 (D) x+y–1= 0, x+2y – 4 = 0

4. The angle between the tangents drawn from a point ( – a, 2a) to y2 = 4 ax is

   
(A) (B) (C) (D)
4 2 3 6

5. The angle between the tangents drawn from a point ( – a, 2a) to y2 = 4 ax is

   
(A) (B) (C) (D)
4 2 3 6

6. The line 4x  7y + 10 = 0 intersects the parabola, y2 = 4x at the points A & B. The co-ordinates
of the point of intersection of the tangents drawn at the points A & B are:
7 5  5 7 5 7  7 5
(A)  ,  (B)   ,   (C)  ,  (D)   ,  
2 2 2 2   2 2 2 2 

7. The feet of the perpendicular drawn from focus upon any tangent to the parabola,
y = x2  2x  3 lies on
(A) y + 4 = 0 (B) y = 0 (C) y = – 2 (D) y + 1 = 0

8. The locus of the middle points of the focal chords of the parabola, y2 = 4x is:
DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-82

 (A) y2 = x  1 (B) y2 = 2 (x  1) (C) y2 = 2 (1  x) (D) none of these

9. The equaton of chord of parabola y2=4x whose midpoint is (2,2)

(A) 2x – 2y + 5= 0 (B) y=x
(C) 2y + 2x + 5= 0 (D) 2y – 2x + 5= 0

10. Suppose two tangents drawn to a parabola at points A and B on it are x + y + 2 = 0 and
x – y + 4 = 0. While the normals drawn at A and B meet at C(1,2) lying on its axis, then
(A) Equation of axis of parabola is x – 4y + 7 = 0.
(B) Length of Latus rectum of parabola is 17 .
(C) Equation of axis of parabola is x + 4y – 9 = 0
(D) Length of Latus rectum of parabola is 15 .

 3
11. If the normals to the curve y = x2 at the points P, Q and R pass through the point  0,  , and
 2
2 2
the equation of the circle circumscribing the triangle PQR is x + y + 2gx + 2fy + c = 0, then
find the value of (g2 + f2 + c2)

Paragraph for question nos. 12 to 14

Consider the parabola x2 = 4y and circle C : x2 + (y – 5)2 = r2 (r > 0). Given that the circle C
touches the parabola at the points P and Q.

12. Radius of the circle C is

(A) 2 (B) 3 (C) 4 (D) 5

13. The distance between chord PQ and directrix of the parabola is

5 4
(A) (B) 3 (C) 4 (D)
3 3

14. The equation of the circle which passes through the vertex of the parabola x2 = 4y and
touches it at the point M (– 4, 4) , is
(A) x2 + y2 – 10x – 18y = 0 (B) x2 + y2 – 8x – 16y = 0
2 2
(C) x + y + 8x = 0 (D) x2 + y2 – 8y = 0

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-83

 ANSWER KEY
DPP-1
1. (A) 2. (C) 3. (A, C) 4. (D) 5. (C) 6. (D) 7. (B)

8. (D) 9. (A) 10. (A) 11. (C) 12. (C) 13. (B) 14. (B)

15. (A) 16. (D) 17. (A,C,D)

DPP-2
1. (B) 2. (A) 3. (C) 4. (A) 5. (ABD) 6. (A) 7. (B)

8. (C) 9. (A) 10. (D) 11. (A) 12. (C) 13. (C)

DPP-3
1. (B) 2. (A) 3. (A) 4. (D) 5. (D) 6. (C) 7. (D)

8. (C) 9. (C) 10. (A) 11. (D) 12. (A) 13. (ABC) 14. (200)

15. (B) 16. (D) 17. (C)

DPP-4
1. (A) 2. (D) 3. (C) 4. (B) 5. (D) 6. (B) 7. (C)

8. (D) 9. (ABCD)10. (AC) 11. (ABC) 12. (0004) 13. (A)

14. (C) 15. (B)

DPP-5
1. (C) 2. (B) 3. (C) 4. (B) 5. (B) 6. (C) 7. (A)

8. (B) 9. (B) 10. (AB) 11. (1) 12. (C) 13. (C) 14. (B)

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE PAGE NO. 101

: www.atpstar.com
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORM AT IO
NO. 01
ELLIPSE
TOPIC : BASIC, EQUATION, ECCENTRIC ANGLE, AUXILLIARY CIRCLE

x2 y2
1. Eccentricity of the conic   1 is
4 9
2 5 7 1
(A) (B) (C) (D)
3 3 3 2
x2 y 2
2. The focii of the ellipse   1 are
25 9
(A) (±4, 0) (B) (±3,0) (C) (± 5,0) (D) (±2,0)

3. The equation of the ellipse whose focus is (1, –1), directrix is the line x – y – 3 = 0 and the
1
eccentricity is , is
2
(A) 7x2 + 2xy + 7y2 – 10x + 10y + 7 = 0 (B) 7x2 + 2xy + 7y2 + 7 = 0
(C) 7x2 + 2xy + 7y2 + 10x – 10y – 7 = 0 (D) none of these

4. The eccentricity of the ellipse 4x2 + 9y2 + 8x + 36y + 4 = 0 is

5 3 2 5
(A) (B) (C) (D)
6 5 3 3

5. If distance between the directrices be thrice the distance between the focii, then eccentricity of
ellipse is
1 2 1 4
(A) (B) (C) (D)
2 3 3 5

6. The length of the latus rectum of the ellipse 9x2 + 4y2 = 1, is

3 8 4 8
(A) (B) (C) (D)
2 3 9 9
x y
7. The eccentricity of the ellipse which meets the straight line + = 1 on the axis of x and the
7 2
x y
straight line – = 1 on the axis of y and whose axes lie along the axes of coordinates is
3 5
6 4 6 2 6 2 6
(A) (B) (C) (D)
7 7 5 7

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-103

8. Equation of the ellipse whose foci are (2, 2) and (4, 2) and the major axis is of length 10 is
(x  3)2 (y  2)2 (x  3)2 (y  2)2
(A) + =1 (B) + =1
4 5 24 25
(x  3)2 (y  2)2 (x  3)2 (y  2)2
(C) + =1 (D) + =1
25 24 25 24

9. The length of the axes of the conic 9x2 + 4y2 – 6x + 4y + 1 = 0, are

1 2 2
(A) ,9 (B) 3, (C) 1, (D) 3, 2
2 5 3

10. An ellipse has OB as semi-minor axis, F and F are its foci and FBF is a right angle then
eccentricity of the ellipse is
1 1 2 1
(A) (B) (C) (D)
2 2 3 3

11. The eccentricity of an ellipse in which distance between their focii is 10 and that of focus and
corresponding directrix is 15 is
1 1 1 1
(A) (B) (C) (D)
3 2 4 2

12. If P = (x, y), F1 = (3, 0), F2 = (3, 0) and 16x2 + 25y2 = 400, then PF1 + PF2 equals
(A) 8 (B) 6 (C) 10 (D) 12

13. If focus and corresponding directrix of an ellipse are (3, 4) and x + y – 1 = 0 and eccentricity
1
is then the co-ordinates of extremities of major axis are
2
(A) (2, 3), (4, 7) (B) (6, 7), (2, 3) (C) (1, 3), (2, 3) (D) (4, 7), (6, 7)

x2 y2
14. If the line lx + my + n = 0 cuts the ellipse + = 1 in two points whose eccentric
a2 b2

angles differ by , then
2
(A) a2l2 + b2n2 = 2 m2 (B) a2m2 + b2l2 = 2 n2 (C) a2l2 + b2m2 = 2 n2 (D) a2n2 + b2m2 = 2 l2
15. If ends of latus rectum of parabola (x + 1)2 = 4(y + 1) are vertices of an ellipse whose
eccentricity is half of eccentricity of parabola, then for ellipse,
(A) distance between foci is 2.
(B) foci are (0, 0) and (2, 0).
(C) length of latus rectum is 3.
(D) combined equation of directrices are (x – 3)(x + 5) = 0.

16. A point moves so that the sum of the squares of its distances from two intersecting straight
lines is constant. Prove that its locus is an ellipse.

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-104

 M AT HEM AT I CS

DPP
DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 02
ELLIPSE
TOPIC : TANGENT OF ELLIPSE, PROPERTIES OF TANGENT,
DIRECTOR CIRCLE

x2 y 2
1. The position of point (4, 3) with respect to the ellipse   1 is
8 9
(A) Out side the ellipse (B) In side the ellipse
(C) On the ellipse (D) On the major axis of ellipse

2. The position of the point (1, 3) with respect to the ellipse 4x2 + 9y2 – 16x – 54y + 61 = 0 is
(A) outside the ellispe (B) on the ellipse
(C) on the major axis (D) on the minor axis
x2 y2
3. If the line y = 2x + c be a tangent to the ellipse + = 1, then c is equal to
8 4
(A) ± 4 (B) ± 6 (C) ± 1 (D) ± 8

4. If the line 3x + 4y =  7 touches the ellipse 3x2 + 4y2 = 1 then, the point of contact is
 1 1   1 1   1 1   1 1 
(A)  ,  (B)  ,  (C)  ,  (D)  , 
 7 7  3 3  7 7  7 7
x2 y2
5. The equation of tangent to the ellipse + =1 which passes through a point (15, – 4) is
50 32
(A) 4x + 5y = 40 (B) 4x + 35y = 200 (C) 4x – 5y = 40 (D) none of these

x2 y2
6. The tangents at the point P on the ellipse  = 1 and its corresponding point Q on the
a2 b2
auxiliary circle meet on the line :
(A) x = a/e (B) x = 0 (C) y = 0 (D) x = –a/e

x2 y2
7. The minimum area of triangle formed by the tangent to the ellipse 2
+ =1 and coordinate
a b2
axes is
a2  b2
(A) ab sq. units (B) sq. unit
2
(a  b)2 a2  ab  b2
(C) sq. units (D) sq. units
2 3
DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-105

 x
8. If the circle x2 + y2 – 2x – 4y + k = 0 and director circle of ellipse + y2 = 1 intersects
4
orthogonally then k equals
(A) 0 (B) 5 (C) – 5 (D) 2

9. If the tangent to the ellipse x2 + 4y2 = 16 at P(4 cos , 2sin) is also normal to circle
x2 + y2 = 8x + 4y, then  can be
  7
(A) (B) (C) 0 (D)
2 4 4

10. The eccentric angle of any point P on the ellipse is . If S is the focus nearest to the end A of
the major axis A'A such that ASP = . Prove that
 1 e 
tan  tan
2 1 e 2

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-106

 M AT HEM AT I CS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN + ADVANCED)

EST INF ORMA TIO
NO. 03
ELLIPSE
TOPIC : NORMAL TO ELLIPSE & ITS PROPERTIES, REFLECTION PROPERTRY

8 y2
1. The value of , for which the line 2x – y = – 3 is a normal to the conic x2 + = 1 is
3 4
3 1 3 3
(A) ± (B) ± (C) – (D) ±
2 2 4 8
2. The eccentric angle of the point where the line, 5x – 3y = 8 2 is a normal to the ellipse
x2 y2
+ =1 is
25 9
   
(A) (B) (C) (D)
4 2 3 6
x2 y2
3. The equation of the normal to the ellipse + = 1 at the positive end of latus rectum is
a2 b2
(A) x + ey + e2a = 0 (B) x – ey – e3a = 0 (C) x – ey – e2a = 0 (D) none of these

x2 y 2
4. If the normal at the point P() to the ellipse  = 1 intersects it again at the point Q(2),
14 5
then cosis equal to
2 2 3 3
(A) (B) – (C) (D) –
3 3 2 2
x2 y2
5. If the normal at an end of a latus-rectum of an ellipse + = 1 passes through one
a2 b2
extremity of the minor axis, then the eccentricity of the ellipse is given by the relation
3
(A) e4 + 2e2 – 4 = 0 (B) e4 + e2 – 1 = 0 (C) e4 + e2 – =0 (D) e4 – e2 – 1 = 0
2
x2 y 2
6. The pair of tangents drawn from the point (4,3) to the ellipse   1 is
16 9
(A) 3x + 4y – xy – 12 = 0 (B) x2 + y2 –3x+ 4y – 12 = 0
(C) 4x + 3y + xy + 12 = 0 (D) x2 + y2 + 2xy +2x+2y+1= 0

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-107

 x2 y2
7. A triangle ABC right angled at 'A' moves so that its sides touch the curve + =1 all the
a2 b2
time. The locus of the point 'A' is
(A) x2 + y2 = 2a2 (B) x2 + y2 = 2b2 (C) x2 + y2 = a2 + b2 (D) none of these

8. If F1 & F2 are the feet of the perpendiculars from the focii S1 & S2 of an ellipse
x2 y2
 = 1 on the tangent at any point P on the ellipse, then (S1F1). (S2F2) is equal to :
5 3
(A) 2 (B) 3 (C) 4 (D) 5

(x  1)2 (y  2)2
9. A ray emanating from (6, 2) is incident on ellipse + = 1 at (4, 6).
45 20
The equation of reflected ray (after 1st reflection) is
(A) x – 2y + 8 = 0 (B) x + 2y + 8 = 0 (C) x + 2y – 8 = 0 (D) x – 2y – 8 = 0

1 
10. The equation of chord of the ellipse 2x2+y2= 2 whose midpoint is  ,1
2 
3 3 5 5
(A) x+y = (B) 2x+y = (C) x+2y = (D) x+y =
2 2 2 2

11. A ray emanating from the point (–3, 0) is incident on the ellipse 16x2 + 25y2 = 400 at the point
P with ordinate 4. Find the equation of the reflected ray after first reflection.
(A) x + y = 12 (B) 3x+ 4y = 11 (C) 4x + 3y = 12 (D) None of these

12. If the normals at P(x1, y1), Q(x2, y2) and R(x3, y3) to the ellipse are concurrent, then prove that
x1 y1 x1 y1
x 2 y2 x 2 y2  0 .
x 3 y3 x 3 y3

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE : www.atpstar.com PAGE NO.-108

 ANSWER KEY
DPP-1
1. (B) 2. (A) 3. (A) 4. (D) 5. (C) 6. (C) 7. (D)
8. (D) 9. (C) 10. (B) 11. (B) 12. (C) 13. (B) 14. (C)
15. (ACD)
DPP-2
1. (A) 2. (C) 3. (B) 4. (D) 5. (A) 6. (C) 7. (A)
8. (B) 9. (AC)
DPP-3
1. (A) 2. (A) 3. (B) 4. (B) 5. (B) 6. (A) 7. (C)
8. (B) 9. (A) 10. (A) 11. (C)

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE PAGE NO. 125

: www.atpstar.com
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN+ADVANCED)
EST INF ORM AT IO
NO. 01
HYPERBOLA

1. The eccentricity of the conic represented by x2 – y2 – 4x + 4y + 16 = 0 is

(A) 1 (B) 2 (C) 2 (D) 1/2

x2 y2
2. The length of latus rectum of the hyperbola – = 1, is
9 16
16 32
(A) (B) (C) 8 (D) 6
3 3

3. The equation of the hyperbola whose conjugate axis is 5 and the distance between the focii is
13, is
(A) 25x2 – 144 y2 = 900 (B) 144 x2 – 25 y2 = 900
(C) 144 x2 + 25 y2 = 990 (D) 25x2 + 144 y2 = 900

4. The equation of the hyperbola whose directrix is x + 2y = 1, focus (2,1) and eccentricity 2 will
be
(A) x2 – 16xy – 11 y2 – 12x + 6y + 21 = 0 (B) 3x2 + 16xy + 15 y2 – 4x – 14y – 1 = 0
2 2
(C) 3x + 16xy + 11 y – 12x – 6y + 21 = 0 (D) None of these

x2 y2
5. The hyperbola – = 1 passes through the point (2, 3) and has the eccentricity 2. Then
a2 b2
the transverse axis of the hyperbola has the length
(A) 1 (B) 3 (C) 2 (D) 4

6. Which of the following is true for the hyperbola x2 – 4y2 = 16 ?

(A) length of transverse Axis = 2 (length of conjugate Axis)
(B) distance between the focii = 4 5
(C) length of latus rectum = 2
(D) distance between the vertices = 8

7. The co-ordinates of the centre of the hyperbola, x2 + 3xy + 2y2 + 2x + 3y + 2 = 0 is

(A) ( 1, 0) (B) (1, 0) (C) ( 1, 1) (D) (1,  1)

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
UNLIMITED PRACTICE FOR FREE
: www.atpstar.com PAGE NO.-126
 (x  2y  4)2
8. The equation (x – 2)2 + (y + 4)2 = 25 represents
5
(A) parabola (B) ellipse (C) Hyperbola (D) Pair of lines

x2 y2
9. The latus rectum of the conic – = 1 is
b2 a2
2b2 2a2
(A) (B) 2a(e2 – 1) (C) (D) 2b (e2 – 1)
a b

10. For hyperbola x2 sec2 – y2 cosec2 = 1, which of the following remains constant with change
in ''
(A) abscissae of vertices (B) abscissae of foci
(C) eccentricity (D) directrix

11. If any point on a hyperbola has the coordinates (5 tan , 4 sec ), then the eccentricity of the
hyperbola
5 41 41 25
(A) (B) (C) (C)
4 5 4 16

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
UNLIMITED PRACTICE FOR FREE
: www.atpstar.com PAGE NO.-127
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN+ADVANCED)
EST INF ORM AT IO
NO. 02
HYPERBOLA

1. Which of the following pair, may represent the eccentricities of two conjugate hyperbolas, for
all  (0, /2) ?
(A) sin , cos  (B) tan , cot 
(C) sec , cosec  (D) 1 + sin , 1 + cos 

2. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half
the distance between the focii, is :
4 4 2
(A) (B) (C) (D) none of these
3 3 3

3. The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, –2).
The equation of the hyperbola is
4 2 196 2 4 2 196 2
(A) x – y =1 (B) x – y =1
49 51 49 51
4 2 51 2
(C) x – y =1 (D) None of these
49 196

4. The vertices of a hyperbola are at (0, 0) and (10, 0) and one of its foci is at (18, 0). The
equation of the hyperbola is
x2 y2 (x – 5)2 y2
(A) – =1 (B) – =1
25 144 25 144
x 2 (y – 5)2 (y – 5)2 y2
(C) – =1 (D) – =1
25 144 25 144

5. The equation of the directrices of the conic x2 + 2x – y2 + 5 = 0 are

(A) x = ± 1 (B) y = ± 2 (C) y = ± 2 (D) x = ± 3

x2 y 2
6. The equation of auxilary circle of hyperbola – 1
9 16
(A) x2 + y2 = 9 (B) x2 + y2 = 16 (C) x2 + y2 = 41 (D) x2 + y2 = 7

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
UNLIMITED PRACTICE FOR FREE
: www.atpstar.com PAGE NO.-128
 x2 y2 y2 x2
7. If e and e are the eccentricities of the hyperbola – = 1 and – = 1, then the
a2 b2 b2 a2
1 1 
point  ,  lies on the circle :
 e e 
(A) x2 + y2 = 1 (B) x2 + y2 = 2 (C) x2 + y2 = 3 (D) x2 + y2 = 4

8. If P ( 2 sec , 2 tan ) is a point on the hyperbola whose distance from the origin is 6
where P is in the first quadrant then  =
  
(A) (B) (C) (D) None of these
4 3 6

x2 (y – 2)2
9. Foci of the hyperbola – = 1 are
16 9
(A) (5, 2), (–5, 2) (B) (5, 2), (5.–2) (C) (5, 2), (–5, –2) (D) None of these

10. If the eccentricity of a hyperbola is 2, then the eccentricity of its conjugate hyperbola is
3 4 2 3
(A) (B) (C) 4 (D)
4 3 3

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
UNLIMITED PRACTICE FOR FREE
: www.atpstar.com PAGE NO.-129
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN+ADVANCED)
EST INF ORM AT IO
NO. 03
HYPERBOLA

1. The line x + y = a touches the hyperbola x2 – 2y2 = 18, if a is equal to ± b, then value of | b | is
(A) 3 (B) 4 (C) 12 (D) 8

2. Equation of a tangent passing through (2, 8) to the hyperbola 5 x2  y2 = 5 is :

(A) 3 x  y + 2 = 0 (B) 3 x + y – 14 = 0
(C) 23 x  3 y  22 = 0 (D) 3 x  23 y + 178 = 0

x2 y2
3. Tangent at any point on the hyperbola 2
– = 1 cut the axes at A and B respectively. If
a b2
the rectangle OAPB (where O is origin) is completed then locus of point P is given by
a2 b2 a2 b2 a2 b2
(A) 2
– 2
=1 (B) 2
+ 2
=1 (C) 2
– =1 (D) none of these
x y x y y x2

4. The number of possible tangents which can be drawn to the curve 4x2  9y2 = 36, which are
perpendicular to the straight line 5x + 2y 10 = 0 is :
(A) zero (B) 1 (C) 2 (D) 4

5. The equation of the tangent lines to the hyperbola x2  2y2 = 18 which are perpendicular to the
line y = x are :
(A) y = – x + 7 (B) y = x + 3 (C) y = – x – 4 (D) y = – x ± 3

6. Number of non-negative integral values of b for which tangent parallel to line y = x + 1 can
x2 y2
be drawn to hyperbola  = 1 is
5 b2
(A) 16 (B) 2 (C) 3 (D) 4

7. An equation of a tangent to the hyperbola, 16x2 – 25y2 – 96x + 100y – 356 = 0 which makes

an angle with the transverse axis is y = x +  , ( > 0), then 2 is
4
(A) 16 (B) 4 (C) 3 (D) 9

8. Equation of tangent to the hyperbola 2x2 – 3y2 = 6 which is parallel to the line y = 3x + 4 is
(A) y = 3x + 5 (B) y = 3x – 5
(C) y = 3x + 5 and y = 3x – 5 (D) None of these

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
UNLIMITED PRACTICE FOR FREE
: www.atpstar.com PAGE NO.-130
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN+ADVANCED)
EST INF ORM AT IO
NO. 04
HYPERBOLA

1. The locus of the middle points of chords of hyperbola 3x2 – 2y2 + 4x – 6y = 0 parallel to y = 2x
is
(A) 3x – 4y = 4 (B) 3y – 4x + 4 = 0 (C) 4x – 4y = 3 (D) 3x – 4y = 2

x2 y2
2. The chords passing through L(2, 1) intersects the hyperbola – =1 at P and Q. If the
16 9
tangents at P and Q intersects at R then Locus of R is
(A) x – y = 1 (B) 9x – 8y = 72 (C) x + y = 3 (D) None of these

3. The tangents from (1, 2 2 ) to the hyperbola 16x2 – 25y2 = 400 include between them an
angle equal to:
   
(A) (B) (C) (D)
6 4 3 2

4. The number of points from where a pair of perpendicular tangents can be drawn to the
hyperbola,
x2 sec2   y2 cosec2  = 1,  (0, /4), is :
(A) 0 (B) 1 (C) 2 (D) infinite

5. From Point p(2,3) two tangents PA and PB are drawn to the hyperbola x2–y2 – 4x+4y + 16 = 0.
The equation of line AB is
(A) y = 3 (B) y = 2 (C) x = 1 (D) x = 3

6. The equation of chord of the hyperbola x2–2y2 = 2 whose midpoint is (3,1)

(A) 3x –2y+7 = 0 (B) 2x –3y+7 = 0 (C) 2x –3y=7 (D) 3x –2y=7

x2 y2
7. The point of intersection of tangents drawn to the hyperbola – = 1 at the points where it
a2 b2
is intersected by the line x + my + n = 0, is
 a2  b2m   a 2  b 2 n   a2  b2n   a2 b2n 
(A)  ,  (B)  ,  (C)  ,  (D)  , 
 n n   m m   m m   m m 

8. Find the locus of the middle points of the chords of contact of tangents to the hyperbola
x2 – y2 = a2 from the points on its auxiliary circle.
DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
UNLIMITED PRACTICE FOR FREE
: www.atpstar.com PAGE NO.-131
 MATHEMATICS

DPP DAILY PRACTICE PROBLEMS

TARGET : JEE(MAIN+ADVANCED)
EST INF ORM AT IO
NO. 05
HYPERBOLA

1. If e and eare the eccentricities of the ellipse 5x2 + 9y2 = 45 and the hyperbola
5x2 – 4y2 = 45 respectively then ee =
(A) – 1 (B) 1 (C) – 4 (D) 9

2. An ellipse and a hyperbola have the same centre origin, the same foci and the minor-axis of
the one is the same as the conjugate axis of the other. If e1, e2 be their eccentricities
1 1
respectively, then  =
e12 e22
(A) 1 (B) 2 (C) 4 (D) none of these

x2 y2 x 2 y2
3. The ellipse   1 and the hyperbola   1 have in common
25 16 25 16
(A) centre only (B) centre, foci and directries
(C) Centre, foci and vertices (D) centre and vertices only

4. If (, 4) is the orthocentre of the triangle whose vertices lie on the rectangular hyperbola
xy = 16, then  is equal to
(A) 3 (B) 4 (C) 12 (D) 8

5. If (5, 12) and (24, 7) are the focii of a conic passing through the origin then the eccentricity of
conic is
(A) 386 /12 (B) 386 /13
(C) 386 /25 (D) 386 /38 or 386 /12

6. The product of the lengths of the perpendiculars from the two focii on any tangent to the
x2 y2 k , then k is
hyperbola – = 1 is
25 3
(A) 16 (B) 4 (C) 3 (D) 9

x 2 y2
7. x  2y + 4 = 0 is a common tangent to y2 = 4x &  = 1. Then the value of ‘b’ and the
4 b2
other common tangent are respectively
(A) b = 3 ; x + 2y + 4 = 0 (B) b = 3; x + 2y + 4 = 0
(C) b = 3 ; x + 2y  4 = 0 (D) b = 3 ; x  2y  4 = 0

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
UNLIMITED PRACTICE FOR FREE
: www.atpstar.com PAGE NO.-132
8. The equation of common tangent to the parabola y2 = 8x and hyperbola 3x2 – y2= 3 is
(A) 2x ± y + 1 = 0 (B) 2x ± y – 1 = 0
(C) x ± 2y + 1 = 0 (D) x ± 2y – 1 = 0

9. The tangent at the point P on the rectangular hyperbola xy = k2 with centre C intersects the
coordinate axes at Q and R. Locus of the circumcentre of triangle CQR is
(A) x2 + y2 = 2k2 (B) x2 + y2 = k2
2
(C) xy = k (D) None of these

10. The equation to the chord joining two points (x1, y1) and (x2, y2) on the rectangular hyperbola
xy = c2 is:
x y x y
(A) + =1 (B) + =1
x1  x 2 y1  y 2 x1  x 2 y1  y 2
x y x y
(C) + =1 (D) + =1
y1  y 2 x1  x 2 y1  y 2 x1  x 2

x2 y2
11. If a hyperbola passes through the focii of the ellipse + = 1. Its transverse and
25 16
conjugate axes coincide respectively with the major and minor axes of the ellipse and if the
product of eccentricities of hyperbola and ellipse is 1, then
x2 y2
(A) the equation of hyperbola is – =1
9 16
x2 y2
(B) the equation of hyperbola is – =1
9 25
(C) focus of hyperbola is (5, 0)
(D) focus of hyperbola is (5 3 , 0)

x2 y2
12. The foci of a hyperbola coincide with the foci of the ellipse + = 1. Find the equation of
25 9
the hyperbola if its eccentricity is 2.

13. Find the equation of common tangents to the hyperbolas x2 – y2 = 18 and xy = 12.

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005
UNLIMITED PRACTICE FOR FREE
: www.atpstar.com PAGE NO.-133
 ANSWER KEY
ANASWER KEY
DPP-1
1. (B) 2. (B) 3. (A) 4. (A) 5. (C) 6. (1,2,3,4)
7. (A) 8. (C) 9. (C,D) 10. (B) 11. (C)

DPP-2
1. (C) 2. (C) 3. (C) 4. (B) 5. (C) 6. (A) 7. (A)
8. (A) 9. (A) 10. (D)
DPP-3
1. (A) 2. (A) 3. (A) 4. (A) 5. (D) 6. (B) 7. (B)
8. (C)
DPP-4
1. (A) 2. (B) 3. (D) 4. (D) 5. (B) 6. (D) 7. (A)
8. a2 (x2 + y2 ) = (x2 – y2)2
DPP-5
1. (B) 2. (B) 3. (D) 4. (B) 5. (D) 6. (D) 7. (A)
8. (A) 9. (C) 10. (A) 11. (A,C) 12. 2 2
3x – y =12
13. 3x + y ± 12 = 0

DOWNLOAD OUR APP & GET : 353, Rajeev Gandhi Nagar, Instrumentation Limited Colony, Kota, Rajasthan 324005

UNLIMITED PRACTICE FOR FREE PAGE NO. 148

: www.atpstar.com