INNOVATION CLASSES

TEST
Topic:- Circles and Parabola Time:- 1 hr 15 min

Marks:- 100

 Single choice:- (+4,-1)

1. The triangle PQR is inscribed in the circle (d) y 2−10 x−6 y +14=0
x 2+ y 2=25. If Q and R have co-ordinates 5. The length of tangents from P(1,-1) and
( 3 , 4 ) and (−4 , 3 ) respectively, then ∠ QPR Q(3,3) to a circle are √ 2 and √ 6
is equal to : respectively, then the length of tangent
(a) π /2 from R(-2,-7) to the same circle is
(b) π /3 a) √ 41
(c) π /4 b) √ 51
(d) π /6 c) √ 61
2. If a circle of constant radius 3 k passes d) √ 71
through the origin and meets the axes at A 6. If the circle x 2+ y 2+ 4 x +22 y+ c=0 bisects
and B , the locus of the centroid of ∆ OAB the circumference of the circle
is : x 2+ y 2−2 x +8 y −d=0 , then c +d is equal
(a) x 2+ y 2=k 2 to :
(b) x 2+ y 2=2 k 2 (a) 40
(c) x 2+ y 2=3 k 2 (b) 50
(d) x 2+ y 2=4 k 2 (c) 60
3. If the line 3 x−4 y+ λ=0 , ( λ>0 ) touches (d) 70
the circle x 2+ y 2−4 x −8 y−¿ 7. If a circles passes through the point ( a , b )
5=0 at ( a , b ) , then λ+ a+b is equal to and cuts the circle x 2+ y 2=4 orthogonally,
a) −22 then the locus of its centre is :
b) −20 (a) 2 ax+ 2by −( a2 +b 2+ 4 )=0
c) 20 (b) 2 ax+ 2by −( a2 −b2 +4 ) =0
d) 22 (c) 2 ax−2 by−( a2+ b2 +4 ) =0
4. The locus of the centre of a circle which (d) 2 ax−2 by−( a2+ b2 +4 ) =0
touches externally the circle x 2+ y 2−¿
8. The sum of the square of the length of the
6 x−6 y +14=0 and also touches the y-
chord intercepted by the line x + y=¿
axis is given by the equation :
n , n ∈ N on the circle x 2+ y 2=4 is
(a) x 2−6 x−10 y +14=0
a) 11
(b) x 2−10 x−6 y +14=0
b) 22
(c) y 2−6 x−10 y +14=0 c) 33

INNOVATION CLASSES Samir Kumar Jha

(9811624151)
C – 4/89 & 90, First Floor, Sector – 6, Rohini, Near Mount Abu Public School. # 9599163168, 9811624151
 d) none of these 18
9. The four points of intersection of the lines (
(a) 6 ,−
5 )
( 2 x− y +1 )( x−2 y +3 ) =0 with the axes lie
(c)
on a circle whose centre is at the point
−7 5
a) ( ) 4 4
,
( 185 )
(b) 6 ,
3 5 18
b) ( , ) (c) ( , 6 )
4 4 5
9 5 (d) none of these
c) ( , )
4 4 13. If 2 x+ y + λ=0 is a normal to the parabola
5 y 2=−8 x then the value of 𝝀 is :
d) (0 , )
4 (a) −24
10. Tangents drawn from the point P(1,8) to (b) −16
the circle x 2+ y 2−6 x−4 y−11=0 touch (c) −8
the circle at the points A and B. The (d) 24
equation of the circumcircle of the 14. The set of points on the axis of the
triangle PAB is parabola y 2−4 x−2 y +5=0 from which all
a) x 2+ y 2+ 4 x−6 y +19=0 the three normals to the parabola are real
b) x 2+ y 2−4 x −10 y+19=0 is :
c) x 2+ y 2−2 x +6 y −29=0 (a) ( λ , 0 ) ; λ>1
d) x 2+ y 2−6 x−4 y +19=0 (b) ( λ , 1 ) ; λ>3
11. A straight line is drawn through the centre (c) ( λ , 2 ) ; λ>6
of circle x 2+ y 2=2 ax parallel to the straight (d) ( λ , 3 ) ; λ>8
line x +2 y =0 and intersecting the circle at 15. The locus of the mid-point of that chord of
A and B . Then the areas of ∆ AOBis parabola which subtends right angle on the
2
a vertex will be
(a)
√5 a) y 2−2 ax +8 a2 =0
2
a b) y 2=a ( x−4 a )
(b)
√7 c) y 2=4 a ( x−4 a )
a2 d) y 2 +3 ax +4 a2=0
(c)
√3 16. A parabola is drawn with focus at (3,4) and
a2 vertex at the focus of the parabola
(d)
√2 y 2−12 x−¿ 4 y +4=0. The equation of the
12. Tangents are drawn to the circle parabola is
2 2
x + y =12 at the points where it is met by a) x 2−6 x−8 y +25=0
the circle x 2+ y 2−5 x+3 y −¿ b) y 2−8 x−6 y+ 25=0
2=0 the point of intersection of these c) x 2−6 x +8 y−25=0
tangents is d) x 2+ 6 x−8 y−25=0
17. From the point (−1,2 ) tangent lines are drawn
to the parabola y 2=4 x , the area of triangle
formed by chord of contact and the tangents is
given by

INNOVATION CLASSES Samir Kumar Jha

(9811624151)
C – 4/89 & 90, First Floor, Sector – 6, Rohini, Near Mount Abu Public School. # 9599163168, 9811624151
 a) 8 (b) 12/13
b) 8 √3 (c) 28/13
c) 8 √2 (d) none of these
d) none of these 23. If the tangents to the parabola y 2=4 ax at
18. A parabola y=a x2 +bx +c crosses the X-axis the points ( x 1 , y 1 ) and ( x 2 , y 2 ) meet at the
at ( α ,0 ) and ( β ,0 ) both to the right of the
point ( x 3 , y 3 ) then :
origin. A circle also passes through these two
points. The length of a tangent from the origin (a) y 3= √ y 1 y 2
to the circle is (b) 2 y 3= y 1 + y 2
bc 2 1 1
a)
√
a
b) ac 2
(c) = +
y3 y1 y2
(d) none of these
b 24. Let P be a point ( 1 , 0 ) and Q a point on the
c)
a locus y 2=8 x . The locus of mid point of
c PQ :
d)
√
a
19. The vertex of the parabola whose parametric
(a) x 2−4 y+ 2=0
(b) x 2+ 4 y +2=0
equation is x=t 2−t+ 1, y=t 2 +t+ 1, t ∈ R ,is (c) y 2 +4 x +2=0
a) (1,1) (d) y 2−4 x+ 2=0
b) (2,2) 25. The angle between the tangents drawn
c) (3,3) from the point ( 1 , 4 ) to the parabola
d) ( 12 , 12 ) y 2=4 x is :
π
20. The shortest distance between the parabolas (a)
6
2 y 2=2 x−1 and 2 x 2=2 y−1 is π
1 (b)
4
a)
2√ 2 π
(c)
1 3
b)
2 π
(d)
c) 2 √2 2
d) 4
21. Let O be the vertex and Q be any point on the
parabola x 2=8 y . If the points P divides the
line segment OQ internally in the ratio 1 : 3,
then the locus of P is
a) x 2= y
b) y 2=x
c) y 2=2 x
d) x 2=2 y
22. The length of the latus rectum of the
parabola 169 {( x−1 )2 + ( y−3 )2}=¿
( 5 x−12 y+17 )2 is :
(a) 14 /13

INNOVATION CLASSES Samir Kumar Jha

(9811624151)
C – 4/89 & 90, First Floor, Sector – 6, Rohini, Near Mount Abu Public School. # 9599163168, 9811624151
INNOVATION CLASSES Samir Kumar Jha
(9811624151)
C – 4/89 & 90, First Floor, Sector – 6, Rohini, Near Mount Abu Public School. # 9599163168, 9811624151