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Parabola

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  1. 51.Let the tangent to the parabola y^2=12x at the point (3, ) be perpendicular to the line 2x…
  2. 52.Let a common tangent to the curves y^2 = 4x and (x - 4)^2 + y^2 = 16 touch the curves at t…
  3. 53.The ordinates of the points P and Q on the parabola with focus (3,0) and directrix x=-3 ar…
  4. 54.Let the tangent to the curve x^2+2x-4y+9=0 at the point P(1,3) on it meet the y-axis at A.
  5. 55.Let S be the set of all a N such that the area of the triangle formed by the tangent at th…
  6. 56.Consider the parabola P: y^2=4kx and the ellipse E:x^2a^2+y^2b^2=1.
  7. 57.An ellipse has its centre at (1,-2), one focus at (3,-2), and one vertex at (5,-2).
  8. 58.Let A, B, and C be the vertices of a variable right-angled triangle inscribed in the parab…
  9. 59.Let O be the vertex of the parabola x^2=4y and Q be any point on it.
  10. 60.If the chord joining the points P_1(t_1) and P_2(t_2) on the parabola y^2=12x subtends a r…
  11. 61.Let the locus of the midpoint of a chord through the origin of the parabola y^2=4x be the …
  12. 62.An equilateral triangle OAB is inscribed in the parabola y^2=4x with the vertex O at the v…
  13. 63.Let A be the focus of the parabola y^2=8x.
  14. 64.Let the directrix of the parabola P: y^2=8x cut the x-axis at the point A.
  15. 65.Let chord PQ of the parabola y^2=12x have length 3√13, such that the ordinates of points P…
  16. 66.Let O be the vertex of the parabola y^2=4x, and let its chords OP and OQ be perpendicular …
  17. 67.Let P be a moving point on the circle x^2+y^2-6x-8y+21=0.
  18. 68.Consider a hyperbola x^2a^2-y^2b^2=1 having one of its foci at P(-3,0).
  19. 69.If the line 3x-2y+12=0 intersects the parabola 4y=3x^2 at the points A and B, then at the …
  20. 70.If the equation of the parabola with vertex V(32,3) and directrix x+2y=0 is x^2+ y^2- xy-3…
  21. 71.Let the focal chord PQ of the parabola y^2=4x make an angle of 60^ with the positive x-axi…
  22. 72.Let the point P of the focal chord PQ of the parabola y^2=16x be (1,-4).
  23. 73.The axis of a parabola is the line x+y=0, and its vertex and focus are in the first quadra…
  24. 74.Let P be the parabola whose focus is (-2,1) and directrix is 2x+y+2=0.
  25. 75.The focus of the parabola y^2=4x+16 is the centre of a circle C of radius 5.
  26. 76.The area (in square units) of the region bounded by the parabola y^2=4(x-2) and the line y…
  27. 77.The area of the region enclosed by the parabola (y-2)^2=x-1, the line x-2y+4=0, and the po…
  28. 78.The area of the region enclosed by the parabola y=4x-x^2 and 3y=(x-4)^2 is equal to:
  29. 79.Let A(,0) and B(0,) be points on the line 5x+7y=50.
  30. 80.Let P be a parabola with vertex (2,3) and directrix 2x+y=6.
  31. 81.Let the latus rectum of a hyperbola (equation not preserved) subtend an angle of 3 at the …
  32. 82.Let P(,) be a point on the parabola y^2=4x.
  33. 83.The sum of squares of all possible values of k, for which the area of the region bounded b…
  34. 84.Three points O(0,0), P(a,a^2), Q(-b,b^2), a>0, b>0, lie on the parabola y=x^2.
  35. 85.Let a tangent to the curve y^2=24x meet the curve xy=2 at the points A and B.
  36. 86.If the area enclosed by the parabolas P_1:2y=5x^2 and P_2:x^2-y+6=0 is equal to the area e…
  37. 87.Let T and C respectively be the transverse and conjugate axes of the hyperbola 16x^2-y^2+6…
  38. 88.The urns A, B, and C contain 4 red, 6 black; 5 red, 5 black; and red, 4 black balls respec…
  39. 89.If P(h,k) is a point on the parabola x=4y^2 which is nearest to the point Q(0,33), then th…
  40. 90.The distance of the point (6,-2√2) from the common tangent y=mx+c, m>0, of the curves x=2y…
  41. 91.Let R be the focus of the parabola y^2=20x, and the line y=mx+c intersect the parabola at …
  42. 92.The area (in sq.
  43. 93.The area of the region enclosed between the parabolas y^2=2x-1 and y^2=4x-3 is:
  44. 94.Let the hyperbola H:x^2a^2-y^2=1 and the ellipse E:3x^2+4y^2=12 be such that the length of…
  45. 95.A particle is moving in the xy-plane along a curve C passing through the point (3,3).
  46. 96.Let P_1 be a parabola with vertex (3,2) and focus (4,4), and P_2 be its mirror image with …
  47. 97.Let x=2t, y=t^23 be a conic.
  48. 98.A circle of radius 2 units passes through the vertex and the focus of the parabola y^2=2x …
  49. 99.If the equation of the parabola, whose vertex is at (5,4) and directrix is 3x+y-29=0, is x…
  50. 100.If the vertex of a parabola is (2,-1) and the equation of its directrix is 4x-3y=21, then …