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  1. 51.A point (2h+1,,3k+2) lies on the circle x^2+y^2=4, while the point (h,k) lies on a circle …
  2. 52.Let A be the point (3,0), and let circles with variable diameter AB touch the fixed circle…
  3. 53.Let each of the two ellipses E_1:x^2a^2+y^2b^2=1 (a>b) and E_2:x^2A^2+y^2B^2=1 (A<B) have …
  4. 54.Let the length of the latus rectum of an ellipse x^2a^2+y^2b^2=1 (a>b) be 30.
  5. 55.Let an ellipse x^2a^2+y^2b^2=1, a<b, pass through the point (4,3) and have eccentricity √5…
  6. 56.Let a focus of the ellipse E:x^2a^2+y^2b^2=1 be S(4,0) and its eccentricity be 45.
  7. 57.Let x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is …
  8. 58.For some (0,2), let the eccentricity and the length of the latus rectum of the hyperbola x…
  9. 59.Let the ellipse E:x^2144+y^2169=1 and the hyperbola H:x^216-y^2^2=-1 have the same foci.
  10. 60.Let the eccentricity e of a hyperbola satisfy 6e^2-11e+3=0.
  11. 61.The eccentricity of an ellipse E with centre at the origin is √32 and its directrices are …
  12. 62.Let E_1: x^29+y^24=1.
  13. 63.The length of the chord of the ellipse x^24+y^22=1, whose midpoint is (1,12), is:
  14. 64.If the midpoint of a chord of the ellipse x^29+y^24=1 is (√2,43), and the length of the ch…
  15. 65.Let the ellipses E_1:x^2a^2+y^2b^2=1 (a>b) and E_2:x^2A^2+y^2B^2=1 (A<B) have the same ecc…
  16. 66.If x+ y=109 is the equation of the chord of the ellipse x^29+y^24=1, whose midpoint is (52…
  17. 67.If S and S' are the foci of the ellipse x^218+y^29=1 and P is a point on the ellipse, then…
  18. 68.Let C be the circle of minimum area enclosing the ellipse E:x^2a^2+y^2b^2=1 with eccentric…
  19. 69.The length of the latus rectum of the ellipse, whose foci are (2,5) and (2,-3) and eccentr…
  20. 70.The centre of a circle C is at the centre of the ellipse E:x^2a^2+y^2b^2=1, a>b.
  21. 71.Let p be the number of all triangles that can be formed by joining the vertices of a regul…
  22. 72.Let e_1 and e_2 be the eccentricities of the ellipse x^2b^2+y^225=1 and the hyperbola x^21…
  23. 73.Let C be the circle x^2+(y-1)^2=2, and E_1,E_2 be two ellipses whose centres lie at the or…
  24. 74.The length of the chord of an ellipse whose midpoint is (1,25), is equal to:
  25. 75.Let e_1 be the eccentricity of a hyperbola (equation not preserved) and e_2 be the eccentr…
  26. 76.If the foci of a hyperbola are the same as those of an ellipse (equation not preserved), a…
  27. 77.Let the foci and length of the latus rectum of an ellipse (details not preserved) be given…
  28. 78.Let P be a point on an ellipse (equation not preserved).
  29. 79.Let an ellipse (equation not preserved) have eccentricity 1√2 and latus rectum √14.
  30. 80.Let C be the largest circle centred at (2,0) and inscribed in the ellipse x^236+y^216=1.
  31. 81.If the maximum distance of a normal to the ellipse x^24+y^2b^2=1, b<2, from the origin is …
  32. 82.The foci of a hyperbola are (2,0) and its eccentricity is 32.
  33. 83.Let the eccentricity of an ellipse x^2a^2+y^2b^2=1 be reciprocal to that of the hyperbola …
  34. 84.Let the ellipse E:x^2+9y^2=9 intersect the positive x- and y-axes at points A and B respec…
  35. 85.Let a circle of radius 4 be concentric to the ellipse 15x^2+19y^2=285.
  36. 86.Consider ellipses E_k:kx^2+k^2y^2=1, k=1,2,,20.
  37. 87.Let P(2√3√7,6√7), Q, R, and S be four points on the ellipse 9x^2+4y^2=36.
  38. 88.Let the maximum area of the triangle that can be inscribed in the ellipse x^2a^2+y^24=1, a…
  39. 89.The line y=x+1 meets the ellipse x^24+y^22=1 at two points P and Q.
  40. 90.The locus of the midpoint of the line segment joining the point (4,3) and points on the el…
  41. 91.Let the eccentricity of an ellipse x^2a^2+y^2b^2=1, a>b, be 14.
  42. 92.For the hyperbola H:x^2-y^2=1 and the ellipse E:x^2a^2+y^2b^2=1, a>b>0, let (1) the eccent…
  43. 93.Let a line L pass through the point of intersection of the lines bx+10y-8=0 and 2x-3y=0, b…
  44. 94.If the ellipse x^2a^2+y^2b^2=1 meets the line x7+ y2√6=1 on the x-axis and the line x7- y2…
  45. 95.If the length of the latus rectum of the ellipse x^2+4y^2+2x+8y-=0 is 4, and l is the leng…
  46. 96.Let the tangents at the points P and Q on the ellipse x^22+y^24=1 meet at the point R(√2,2…
  47. 97.A ray of light through (2,1) is reflected at a point P on the Y-axis and then passes throu…
  48. 98.Let an ellipse E:x^2a^2+y^2b^2=1, a^2>b^2, pass through (32,1) and have eccentricity 1√3.
  49. 99.If a tangent to the ellipse x^2+4y^2=4 meets the tangents at the extremities of its major …
  50. 100.Let E_1:x^2a^2+y^2b^2=1, a>b.