1.

The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2= 9 is
 3 1  1 3
(A)  ,  (B)  , 
 2 2  2 2
 1 1 1 
(C)  ,  (D)  ,  2 
 2 2 2 

2. The coordinates of mid point of the chord cut off by 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)

3. Equation of tangent drawn from origin to the circle x2 + y2 – 2rx + 2hy + h2 = 0 are
(A) x = 0 (B) y = 0
(C) (h2 – r2)x – 2rhy = 0 (D) (h2 – r2)x + 2rhy = 0
4. If 2 circles (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect at 2 distinct points, then
(A) 2 < r < 8 (B) r > 2
(C) r = 2 (D) r < 2

5. The equation of circle passing through (1, –3) and the points common to the two circles
x2 + y2 – 6x + 8y – 16 = 0, x2 + y2 + 4x – 2y – 8 = 0 is
(A) x2 + y2 – 4x + 6y + 24 = 0 (B) 2x2 + 2y2 + 3x + y – 20 = 0
2 2
(C) 3x + 3y – 5x + 7y – 19 = 0 (D) none of these

6. The common chord of x2+ y2– 4x –4y = 0 and x2 + y2 = 16 subtends at the origin an angle equal to
 
(A) (B)
6 4
 
(C) (D)
3 2

7. The locus of the centre of the circle which touches externally the circle x2+y2–6x–6y+14=0 and
also touches the y-axis is given by the equations
(A) x2 – 6x – 10y + 14 = 0 (B) x2 – 10x – 6y + 14 = 0
2
(C) y – 6x – 10y + 14 = 0 (D) y2 – 10x – 6y + 14 = 0

8. If the tangent at the P on the circle x2 + y2 + 2x + 2y = 7 meets the straight line 3x – 4y = 15 at a

point Q on the x-axis, then length of PQ is
(A) 3 7 (B) 4 7
(C) 2 7 (D) 7

9. A straight line is drawn through the centre of the circle x2 + y2 – 2ax = 0, parallel to the straight
line x + 2y = 0 and intersecting the circle at A and B. Then the area of AOB is
a2 a3
(A) (B)
5 5
2
a a3
(C) (D)
3 3
Quiz Bank-Circle-4

10. The equation of the circle of radius 2 which touches the line x + y = 1 at (2, –1) is
(A) x2 + y2 – 4x +2y+ 3= 0 (B) x2 + y2 + 6x +7= 0
(C) x2 + y2 – 2x +4y+ 3= 0 (D) none of these

11. If the co–ordinates of one end of a diameters of the circle x2 + y2 – 8x – 4y + c = 0 are (–3, 2),
then the co–ordinates of the other end are
(A) (5, 3) (B) (6, 3)
(C) (1, –8) (D) (11, 2)

12. The equation of the locus of the centre of circles touching the y–axis and circle x2 + y2 –2x= 0 is
(A) x2 = 4y (B) x2 = – 4y
2
(C) y = 4x (S) y2 = – 4x

13. The angle between a pair of tangents drawn from a point P to the circle
x2 + y2 + 4x – 6y + 9 sin2 + 13 cos2 = 0 is 2. The equation of the locus of P is
(A) x2 + y2 + 4x – 6y + 4 = 0 (B) x2 + y2 + 4x – 6y –9 = 0
2 2
(C) x + y + 4x – 6y – 4 = 0 (D) x2 + y2 + 4x – 6y + 9 = 0

14. The number of common tangents to the circles x2 + y2 – 6x – 14y + 48 = 0 and x2 + y2 – 6x = 0 is

(A) 1 (B) 2
(C) 3 (D) 4

15. The equation of the smallest circle passing through the intersection of the line x + y = 1 and the
circle x2 + y2 = 9 is
(A) x2 + y2 + x + y – 8 = 0 (B) x2 + y2 – x – y – 8 = 0
2 2
(C) x + y – x + y – 8 = 0 (D) none of these

16. A, B, C, D are the points of intersection with the co-ordinate axes of the lines ax + by = ab and
bx + ay = ab then
(A) A, B, C, D are concyclic (B) A,B,C,D forms a parallelogram
(C) A, B, C, D forms a rhombus (D) None of these

17. If the lines 2x – 3y – 5 = 0 and 3x-4y = 7 are diameters of a circle of area 154 square units, then
the equation of the circle is
(A) x2+y2+2x-2y-62 = 0 (B) x2+y2+2ax –2y – 47 = 0
2 2
(C) x +y -2x+2y-47 = 0 (D) x2+y2-2x+2y-62 = 0
18. The equation of the circle whose diameter is the common chord of the circle x2+y2+3x+2y+1= 0
and x2+y2+3x+4y+2 = 0 is
(A) x2+y2+8x+10y+2 = 0 (B) x2+y2-5x+4y+7 = 0
(C) 2x2+2y2+6x-2y-1 = 0 (D) None of these

19. The length of the tangent from any point on the circle 15x2 +15y2 – 48x + 64y = 0 to the two
circles 5x2 + 5y2 – 24x + 32y + 75 = 0 and 5x2 + 5y2–48x + 64y + 300 = 0 are in the ratio of
(A) 1 : 2 (B) 2 : 3
(C) 3 : 4 (D) None of these

20. The tangents drawn from the origin to the circle x2+y2-2rx-2hy+h2 = 0 are perpendicular if
(A) h = r (B) h = – r
(C) r2+ h2 = 1 (D) r2 = h25.
 Quiz Bank-Circle-5
21. If a variable circle of radius 4 cuts the circle x2 + y2 = 1 orthogonally then locus of its centre
will be
(A) x2 + y2 = 16 (B) x2 + y2 =17
2 2
(C) x + y - 2x - 4y = 1 (D) 2x - 4y + 5 = 0

 1
22. If four points  t i ,  ( i = 1, 2, 3, 4) are concyclic then t1t2 t3t4 =
 ti 
(A) 1 (B) -1
(C) 4 (D) 1/4

23. The number of common tangents that can be drawn to the circle x2+y2–4x – 6y – 3 = 0 and
x2 + y2 + 2x + 2y + 1 = 0 is
(A) 1 (B) 2
(C) 3 (D) 4

24. The circle x2 + y2 + 2ax + c = 0 and x2 + y2 + 2by + c = 0 touch if

1 1 1 1 1 1
(A) 2  2  (B) 2  2  2
a b c a b c
1 1 1
(C)    0 (D) none of these
a b c

25. The equation (x2 –a2)2 + (y2 –b2)2 = 0 represents points

(A) which are collinear (B) which lie on a circle centred (0, 0)
(C) which lie on a circle centre (a, b) (D) none of these

26. The equations of the circle which touch both the axes and the line x = a are
a2 a2
(A) x2+y2  ax  ay+ =0 (B) x2+y2 + ax  ay+ =0
4 4
a2
(C) x2+y2 -ax  ay+ =0 (D) None of these
4

27. If the abscissae and ordinates of two points P and Q are the roots of the equation x2+2ax-b2 = 0
and x2+2px-q2 = 0 respectively, then the equation of the circle with PQ as diameter is
(A) x2+y2+2ax+2py-b2-q2 = 0 (B) x2+y2-2ax-2py+b2+q2 = 0
2 2 2 2
(C) x +y -2ax-2py-b -q = 0 (D) x2+y2+2ax+2py+b2+q2 = 0

28. If the distances from the origin of the centre of three circles x2+y2 +2ix –c2=0 (i= 1, 2, 3) are in
G.P. then the length of the tangent drawn to them from any point on the circle x2+y2 = c2 are in
(A) A.P. (B) G.P.
(C) H.P. (D) None of these

29. If the chord of contact of tangents drawn from a point on the circle x2 + y2 =a2 to the circle
x2 + y2 = b2 touches the circle x2 + y2 =c2, a, b, c> 0, then a, b, c are related as ……

30. The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have co-ordinates (3, 4) and
(–4, 3) respectively, then QPR is equal to
(A) /2 (B) /3
(C) /4 (D) /6