VMC Mathematics Test: Circles 01. The condition that cx  by  b  0 may touch the circle 2 abc=1 b=ac greatest (B) a = c (D) None of these distance of the point (10,7) from 2 x 2  y 2  16x  55  0 5 (B) 8 (C) 5 5 (D) None of these  ,   is a point on the circle whose centre is on x-axis x  y  0 at and (2, -2) then the greatest value of (B) 4  2 2 circle then area of quadrilateral OACB is 2 1 (A) (B) c g  f c g2  f 2  c 2 (C) c g  f 2 2 (C) x  2 y  4  0 (D) x  y  1  0 06. If O is the origin and OP and OQ are tangents from the origin to circle x  y  6 x  4 y  8  0 , the circum centre of 2 OPQis (B)  3 , 1   (A) (3, -2) 2 (C)  3 ,  1  4 2  (D)  3  ,1   2  and intersecting the circle at A and B. Then the area of (B) 2 (D) 3 a2 7 a 2 (B)  6, 18    (C)  18 , 6  5  (D) None of these  intersection of 5 2 4 (B) (D) (B) x 2  aa  2 y  2 2 2 2 2 and is normal to x  y  4 x  2 y  3  0 then (a, b) = 2 (A) (2, 1) (B) (1, -2) (C) (1, 2) (D) (-1, 2) 17. Let A (x`1, y1) B (x2, y2) circles with OA, OB as diameter drawn. Then the length of the common chord. (A) x1 y 2  x 2 y1 2 AB 2 x1 y 2  x 2 y1 AB (A) x  y  9a (B) x1 y 2  x 2 y1 AB (D) None of these 2 2 (B) x 2  y 2  16a 2 (C) x  y  4a (D) x  y  a 19. The equation of the circle having its centre on the line x  2 y  3  0 and passing through the intersection of the circle x2 + y2 −2x −-4y + 1 = 0 and x2 + y2 −4x −-2y + 4 = 0 is 2 2 2  2  (C) 2 2 2 2 2 2 (A) x  y  6 x  7  0 10. The triangle PQR is inscribed in the circle x  y  25 . If Q & R have coordinates (3, 4) and (-4, 3) respectively then QPR is (A) 2 (C) x  y  x  a  (D) x  y   y  a  15. Two vertices of an equilateral triangle are (-1, 0) and (1, 0) and third vertex lies above the x-axis. The equation of its circum circle. 2x (A) x 2  y 2  2 x  1  0 (B) x 2  y 2  1 0 3 3 2y (C) x 2  y 2  2 y  1  0 (D) x 2  y 2  1 0 3 3 16. The line the circle ax  by  0 touches 2 2 (A)  6, 18   5  c 18. The equation of the circle with origin as centre and passing through the vertices of an equilateral  whose median is of length 3a is 2 by x 2  y 2  5 x  3 y  2  0 , the point of these tangents is    2 2 (C) 09. Tangents are drawn to x  y  12 at points where it is met 2 c g2  f 2 c (D) (A) y  a a  2 x  AOBis a2 5 2 14. The locus of the point of intersection of the tangents at 2 x 2  y 2  2ax parallel to the straight line x  2 y  0 a c x 2  y 2  2x  4 y  0 07. The circle passing through the distinct points (1, t), (t, 1) and (t, t) for all values of t passes through the point. (A) (1, 1) (B) (-1, -1) (C) (1, -1) (D) (-1, 1) 08. A straight line is drawn through the centre of the circle (C) 2 2 the point (2, 3) farthest from the centre is (A) 2 x  3 y  13 (B) 3x  y  3 (A)   touches the circle x  y  2ax  0 is (D) 4  2 2 x 2  y 2  2 gx  2 fy  c  0, ' C ' the centre of the the extremities of a chord of x  y  a which 2 2 05. The equation of the chord of x  y  a passing through (C) 13. If OA and OB are the tangents from origin to the circle 2 4 2 42 2 (A) (D) 0  (A) which touches  is (B)  6 2 (A) 10 (B) 15 (C) 5 (D) None of these 03. The least distance between two points P & Q on the circles 04. If  3  (C) (A) x  y  4 x  2 y  20  0 is 2 x  72   y  12  25 is circle x 2  y 2  ax  by is (A) (C) 02. The 12. The angle between the two tangents from origin to the 2  3  6 11. 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 VMC, 485 – B, McLeod Road, Rani Ka Bagh, Amritsar. 2 (B) x  y  3 x  4  0 2 2 (C) x  y  2 x  2 y  1  0 2 2 (D) x  y  2 x  4 y  4  0 20. The centre of the circle inscribed in a square formed by the lines x28x+12=0 and y214y+45=0 is (A) (4, 7) (B) (7, 4) (C) (9, 4) (D) (4, 9) 21. 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 2 2 Phone: 9779905879. [email protected] Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. d) b) s b) a) b) a) a) a) c) c) c) b) s d) c) c) c) a) a) a) Email: [email protected] , Phones: 0183-2291879, 98146-55879