MATHS BY RUPESH K JHA...

GS ROAD CHRISTIAN BASTI GUWAHATI 1

TO BE SUBMITTED SHEET-

Strenthening your Concept TBS--Ellipse -Ent-1

maths by rupesh k jha.....9864030380
www.infinity4maths.com....7086055586
ASKING DOUBTSARE YOUR FUNDAMENTAL RIGHT,
Lets Revise the Previous Class....it’s not a luxury, it’s a necessity
Q1 Find the equation of the ellipse with its centre (1, 2), focus at (6, 2) and passing through the point (4, 6).

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Q2 Find the equation of the ellipse whose foci are (2, 3), (–2, 3) and whose semi-minor axis is 5 .

om 55
Q3 A ladder 12 units long slides in a vertical plane with its ends in contact with a vertical wall and a horizontal
floor along x-axis. The locus of a point on the ladder 4 units from its foot has the equation :

-c 5
x2 x2 y2 x2 y2 y2
(A) + y2 = 1 (B)  =1 (C)  =1 (D) x2 + =1
4 16 64 64 16 4

hs 60
 5  x2 y2
Q4 Find the set of those value(s) of ‘’ for which the point  7  4 ,   lies inside the ellipse + =1.
  25 16

Q5
at 08
Write the parametric equation of ellipse
(x  3)2
25
+
(y  2)2
16
= 1.
4m ...7
Q6 Find the set of possible value of  for which point P(, 3) lies on the smaller region of the ellipse
9x2 + 16y2 = 144 divided by the line 3x + 4y = 12.

Q7 Find the length of chord x – 2y – 2 = 0 of the ellipse 4x2 + 16y2 = 64.

ity a.

Directrix of Ellipse is x=a/e or x =-a/e and distance between directrix =2a/e

fin Jh

Q.8 If the distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is
(1) 1/2 (2) 2/3 (3) 1/ 3 (4) 4/5
-in k

Q.9 The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is
18, is
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(1) 5x2 – 9y2 = 180 (2) 9x2 + 5x2 = 180 (3) x2 + 9y2 = 180 (4) 5x2 + 9y2 = 180

Q.10 The foci of the conic section 25x2 + 16y2 – 150x = 175, are
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(1) (0, ±3) (2) (0, ±2) (3) (3, ±3) (4) (0, ±1)
x 2 y2
u

Q.11 The equation to the locus of the middle point of the portion of the tangent to the ellipse + =1
16 9
R

included between the co-ordinate axes is the curve :

(1) 9x2 + 16y2 = 4 x2y2 (2) 16x2 + 9y2 = 4 x2y2
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(3) 3x2 + 4y2 = 4 x2y2 (4) 9x2 + 16y2 = x2y2

Q.12 The equation of the tangent to the ellipse x2 + 16y2 = 16 making an angle of 60º with x-axis is
(1) 3x–y+7=0 (2) 3x–y–7=0 (3) 3x–y±7=0 (4) None of these

x 2 y2
Q.13 The line lx + my – n = 0 will be tangent to the ellipse   1 , if
a 2 b2
(1) a2l2 + b2m2 = n2 (2) al2 + bm2 = n2 (3) a2l + b2m = n (4) None of these

DISTRACTIONS MAKE LEARNING HARDER

 MATHS BY RUPESH K JHA... GS ROAD CHRISTIAN BASTI GUWAHATI 2

Q.14 The equation of the tangents of the ellipse 9x2 + 16y2 = 144 which passes through the point (2, 3) is
(1) y = 3, x + y = 5 (2) y = –3, x – y = 5 (3) y = 4, x + y = 3 (4) y = –4, x – y = 3

Q.15 Eccentric angle of a point on the ellipse x2 + 3y2 = 6 at a distance 2 units from the centre of the ellipse is
  3 2
(1) (2) (3) (4)
4 3 4 3

x 2 y2
Q.16 If the area of the auxiliary circle of the ellipse   1 (a > b) is twice the area of the ellipse, then the
a 2 b2

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eccentricity of the ellipse is
1 3 1 1

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(1) (2) (3) (4)
2 2 3 2
Q.17 Let S(5, 12) and S'(– 12, 5) are the foci of an ellipse passing through the origin. The eccentricity of ellipse
equals

-c 5
1 1 1 2

hs 60
(A) (B) (C) (D)
2 3 2 3
x 2 y2
Q.18 F1 and F2 are the two foci of the ellipse   1 . Let P be a point on the ellipse such that

at 08 9 4
PF1  2 PF2 , where F1 and F2 are the two foci of the ellipses. The area of PF1F2 is
4m ...7
13
(A) 3 (B) 4 (C) 5 (D)
2
x 2 y2
Q.19 If the normal at the point P() to the ellipse   1 , intersects it again at the point Q(2),
ity a.

14 5
show that cos = – (2/3).
fin Jh

Q.20 Suppose x and y are real numbers and that x2 + 9y2 – 4x + 6y + 4 = 0 then find the maximum value of
(4x – 9y).
4 x 2 y2
-in k

Q.21 A tangent having slope  to the ellipse   1 , intersects the axis of x & y in points A & B
3 18 32
respectively. If O is the origin, find the area of triangle OAB.
w sh

Q.22 Find the equation of the largest circle with centre (1, 0) that can be inscribed in the ellipse x2 + 4y2 = 16.
w pe

x 2 y2
Q23 Consider the ellipse  = 1 and the parabola y2 = 2x. They intersect at P and Q in the first and
9 4
u

fourth quadrants respectively. Tangents to the ellipse at P and Q intersect the x-axis at R and tangents to the
R

parabola at P and Q intersect the x-axis at S.

w

(i)The ratio of the areas of the triangles PQS and PQR, is

(A) 1 : 3 (B) 1 : 2 (C) 2 : 3 (D) 3 : 4
(ii)The area of quadrilateral PRQS, is
3 15 15 3 5 3 5 15
(A) (B) (C) (D)
2 2 2 2
Q.24 The y-axis is the directrix of the ellipse with eccentricity e = 1/2 and the corresponding focus is at (3, 0),
equation to its auxilary circle is
(A) x2 + y2 – 8x + 12 = 0 (B) x2 + y2 – 8x – 12 = 0
2 2
(C) x + y – 8x + 9 = 0 (D) x2 + y2 = 4
DISTRACTIONS MAKE LEARNING HARDER
 MATHS BY RUPESH K JHA... GS ROAD CHRISTIAN BASTI GUWAHATI 3

Q.25 Given ellipse x2 + 4y2 = 16 and parabola y2 – 4x – 4 = 0 The quadratic equation whose roots are the
slopes of the common tangents to parabola and ellipse, is
(A) 3x2 – 1 = 0 (B) 5x2 – 1 = 0
2
(C) 15x + 2x – 1 = 0 (D) 2x2 – 1 = 0
x 2 y2
Q.26 x  2y + 4 = 0 is a common tangent to y2 = 4x &  2 = 1. Then the value of b and the other common
4 b
tangent are given by :
(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

86
x 2 y2
Q.27 Consider the particle travelling clockwise on the elliptical path  = 1. The particle leaves the orbit
100 25

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at the point (–8, 3) and travels in a straight line tangent to the ellipse. At what point will the particle cross the
y-axis?

-c 5
 25   23   26 
(A)  0,  (B)  0,  (C) (0, 9) (D)  0, 
 3   3  3 

hs 60
x 2 y2
Q.28 The minimum area of a triangle formed by any tangent to the ellipse  = 1 and the coordinate axes
16 81
is
(1) 26at 08 (2) 12 (3) 18 (4) 36
4m ...7
x2 y2
Q.29 The Locus of the middle point of chords of an ellipse   1 passing through P(0, 5)
16 25
is another ellipse E. The coordinates of the foci of the ellipse E, is
 1 
ity a.

 3  3  11 
(A)  0,  and  0,  B) (0, – 4) and (0, 1) (C) (0, 4) and (0, 1) (D)  0,  and  0, 
 5  5   2  2 
fin Jh

Q.30 The area of the quadrilateral formed by the tangents at the ends of the latus rectum of the ellipse
x2 y2
  1 is
-in k

9 5
(A) 9 3 sq. units (B) 27 3 sq. units (C) 27 sq. units (D) none
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1
Q.31 Line L1 is parallel to the line L2. Slope of L1 is 9. Also L3 is parallel to L4. Slope of L4 is .
w pe

25
x 2 y2
All these lines touch the ellipse   1 . Find the area of the parallelogram formed by these lines.
25 9
u

ANSWER KEY
R

Q1. 20x2 + 45y2  40x  180y  700 = 0 Q2. 5x2 + 9y2 – 54y + 36 = 0
w

 12 16  4 4
Q3)C Q4)  5 , 5  Q5(x = 3 + 5cos, y = – 2 + 4sin) Q6 <<
  5 17

Q7 35
Q.8)3 Q9)4 Q10)3 Q11)1 Q12)3 Q13)1 Q14)1
11
Q15)1 Q16)2 Q17C Q18)B Q20)16 Q21)24 Q22)(x  1)2 + y2 =
3
Q23 B Q24)A Q25)B Q26)A Q27)A Q28)4 Q29)C
Q30)C Q31)60
DISTRACTIONS MAKE LEARNING HARDER