Circles
1. If the length of the tangent from any point on the circle (x - 3)2 + (y + 2)2 = 5r2 to the circle (x - 3)2 + (y + 2)2 = r2 is 16 units, then the area between the two circles is
Ans: 256 ∏
2. If the length of transverse common tangent of the circle x2 + y2 = 4 and (x - h)2 + y2 = 1 is 3
, then h =
Ans: 3
3. An angle subtended by the common chord of x2 + y2 − 4x − 4y = 0 and x2 + y2 = 16 at the origin is
Ans: ∏/2
4. Minimum radius of circle which is orthogonal to both the circles x2 + y2 - 12x + 35 = 0 and x2 + y2 + 4x + 3 = 0 is
Ans: 
5. The range of values of 'a' such that the angle θ between the pair of tangents drawn from (a, 0) to the circle x2 + y2 = 1 satisfies 
< θ < 
is
Ans: (−
, −1) 
(1,
)6. If r1 and r2 are radii of the circles whose centres are at a distance '1' unit from the origin and touches the lines y =
(x + 1), then 
=and y = (x + 1), then =Ans: 1
7. If 3x + 4y + 15 = 0 cuts equal intercepts between x2 + y2 = 13, x2 + y2 = r2 and x2 + y2 = 45 45 (
< r < 
), then r =, then r =Ans: 5
8. The locus of all points P whose farthest and shortest distances to the circle (x − a)2 + (y + b)2 = (a + b)2 are 2a, 2b (a > b > 0) is is
Ans: (x - a)2 + (y - b)2 = a2 + b2
9. Let S1 ≡ x2 + y2 − 4x − 8y + 4 = 0 and S2 be its image in the line y = x. The equation of the circle touching y = x at (1, 1) and orthogonal to S2 is
Ans: x2 + y2 + x - 5y + 2 = 0
10. x2 + y2 + 6x + 8y = 0 and x2 + y2 − 4x − 6y − 12 = 0 are the equations of the two circles. Equation of one of their common tangent is
Ans:
= 011. The equation of chord of the circle x2 + y2 − 6x − 4y − 12 = 0 which passes through the origin such that the origin divides it in the ratio 3 : 2 is
Ans: x + y = 0; 7y + 17x = 0
12. The points 'A', 'B' are the feet of O (0, 0) on x − 2y + 1 = 0, 2x − y − 1 = 0 respectively, then the circum radius of the ∆OAB is
Ans: 
13. The locus of the image of the point (2, 3) with respect to the line (x − 2y + 3) + λ (2x − 3y + 4) = 0 (λ 
R) is
Ans: x2 + y2 − 2x − 4y + 3 = 0
14. Let A (1, 2), B (3, 4) be two points and C(x, y) be a point such that area of ∆ABC is 3 sq.units and (x − 1)(x − 3) + (y − 2)(y − 4) = 0, then maximum number of positions of 'C' in the XY plane is
A) 2 B) 4 C) 8 D) No such 'C' exists
Ans: No such 'C' exist
15. If the circle x2 + y2 + 4x + 22y + c = 0 bisects the circumference of the circle x2 + y2 − 2x + 8y − d = 0, then c + d =
Ans: 50
16. The equation of a circle through the intersection of x2 + y2 + 2x = 0 and x − y = 0 having minimum radius is
Ans: x2 + y2 − x − y = 1
17. From a point 'P' outside a circle with centre at 'C' tangents PA and PB are drawn such that 
, then length of chord AB =
Ans: 8 units
18. The chord through (2, 1) to the circle x2 + y2 − 2x − 2y + 1 = 0 is bisected at the point 
, then the value of 'α' =
A) 
B) 1 C) 0 D) None of the above
Ans: None of the above
19. The curve x2 − y − 
x + 1 = 0 intersects X − axis at 'A' and 'B'. A circle is drawn passing through A and B. The length of tangent drawn from the origin to this circle is
A) 
B) 
C) 
D) None of these
Ans: None of these
20. The locus of the mid points of chords of the circle x2 + y2 = 9 such that segment intercepted by the chord on the curve y2 − 4x − 4y = 0 subtends a right angle at the origin is
Ans: x2 + y2 − 4x − 4y = 0
21. Tangents are drawn to the circle x2 + y2 = 10 at the points where it is met by the circle x2 + y2 − 6x − 4y + 10 = 0, then the point of intersection of these tangents is
Ans: (3, 2)
22. The equation of the circle described on the common chord of the circles x2 + y2 − 4x − 5 = 0 and x2 + y2 + 8y + 7 = 0 as a diameter is
Ans: x2 + y2 − 2x + 4y + 1 = 0
23. The area bounded by the circles x2 + y2 = r2; r = 1, 2 and the rays given by 2x2 − 3xy − 2y2 = 0; y > 0 is
Ans: 
24. The points A, B are the feet of O(0, 0) on x − 2y + 1 = 0; 2x − y − 1 = 0 respectively, then the circum radius of ∆OAB is
Ans: 
25. If a circle of radius '3' pass through origin 'O' and meets co-ordinate axes at A and B, then the locus of the centroid of triangle OAB is
Ans: x2 + y2 = 4
26. Tangents PA and PB are drawn to the circle (x + 2)2 + (y − 2)2 = 1 from the points which lie on the line y = x, then the locus of circumcentre of ∆PAB is
Ans: y = x + 2
27. There are exactly two chords of the circle x2 + y2 = 100 that passes through (1, 7) and subtends an angle 
at the origin, then the angle between these two chords is
Ans: 
28. A square is inscribed in the circle x2 + y2 − 2x + 4y + 3 = 0. Its sides are parallel to the coordinate axes, then one vertex of the square is
A) (1 + 
, − 2) B) (1 − 
, − 2) C) (1, − 2 + 
) D) None of these
Ans: None of these
29. The coordinates of a point 'P' on the circle x2 + y2 − 4x − 6y + 9 = 0 such that 
is minimum where 'O' is the origin and OX is the X - axis are
Ans: 
