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Parabola

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  1. 151.The locus of the vertices of the family of parabolas [y = a^3x^2 3 + a^2x 2 - 2a] is :
  2. 152.Given : A circle, 2x^2 + 2y^2 = 5 and a parabola, [y^2 = 4 5 x].
  3. 153.If the common tangents to the parabola, x2 = 4y and the circle, x2 + y2 = 4 intersect at t…
  4. 154.If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 u…
  5. 155.Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the ax…
  6. 156.Tangents drawn from the point (-8, 0) to the parabola y2 = 8x touch the parabola at P and …
  7. 157.Let P be a point on the parabola, x2 = 4y.
  8. 158.If the line ax + y = c, touches both the curves x2 + y2 = 1 and y2 = 4[ 2 ]x , then |c| is…
  9. 159.The length of the chord of the parabola x2 = 4y having equation x -- [ 2 y + 4 2 = 0] is -
  10. 160.If the parabolas y2 = 4b(x -- c) and y2 = 8ax have a common normal, then which on of the f…
  11. 161.If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4(x --…
  12. 162.The equation of common tangent to the curves y2 = 16x and xy = --4, is :
  13. 163.Let P be the point of intersection of the common tangents to the parabola y2 = 12x and the…
  14. 164.The equation of a tangent to the parabola, x2 = 8y, which makes an angle [ ] with the posi…
  15. 165.The maximum area (in sq.
  16. 166.The tangent to the parabola y2 = 4x at the point where it intersects the circle x2 + y2 = …
  17. 167.If one end of a focal chord of the parabola, y2 = 16x is at (1, 4), then the length of thi…
  18. 168.Equation of a common tangent to the circle, x2 + y2 -- 6x = 0 and the parabola, y2 = 4x is…
  19. 169.If [ ] denotes the acute angle between the curves, y = 10 -- x2 and y = 2 + x2 at a point …
  20. 170.Let the latus ractum of the parabola y2 = 4x be the common chord to the circles C1 and C2 …
  21. 171.Let P be a point on the parabola, y2 = 12x and N be the foot of the perpendicular drawn fr…
  22. 172.If the common tangent to the parabolas, y2 = 4x and x2 = 4y also touches the circle, x2 + …
  23. 173.If y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b is equal to…
  24. 174.If one end of a focal chord AB of the parabola y2 = 8x is at [A( 1 2, - 2 )], then the equ…
  25. 175.If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0) a [] 0, …
  26. 176.Consider the parabola with vertex [( 1 2,3 4 )] and the directrix [y = 1 2].
  27. 177.Let P be a variable point on the parabola y = 4x^2 + 1.
  28. 178.If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x - …
  29. 179.The shortest distance between the line x - y = 1 and the curve x2 = 2y is :
  30. 180.A tangent is drawn to the parabola y2 = 6x which is perpendicular to the line 2x + y = 1.
  31. 181.If two tangents drawn from a point P to the parabola y2 = 16(x - 3) are at right angles, t…
  32. 182.The length of the latus rectum of a parabola, whose vertex and focus are on the positive x…
  33. 183.Let x2 + y2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola…
  34. 184.The tangents at the points A(1,3) and B(1,-1) on the parabola y^2-2 x-2 y=1 meet at the po…
  35. 185.If the line [y = 4 + kx,,k > 0], is the tangent to the parabola y = x - x^2 at the point P…
  36. 186.If y = m_1x + c_1 and y = m_2x + c_2, [m_1 m_2] are two common tangents of circle x^2 + y^…
  37. 187.Let the normal at the point on the parabola y2 = 6x pass through the point (5, -8).
  38. 188.Let P(a, b) be a point on the parabola y^2=8 x such that the tangent at P passes through t…
  39. 189.If the tangents drawn at the points [P] and [Q] on the parabola y^2=2 x-3 intersect at the…
  40. 190.Let [PQ] be a focal chord of the parabola y^2=36 x of length 100 , making an acute angle w…
  41. 191.If [P(h, k)] be a point on the parabola x=4 y^2, which is nearest to the point [Q(0,33)], …
  42. 192.Let [y=f(x)] represent a parabola with focus [(-(1)/(2), 0)] and directrix [y=-(1)/(2)].
  43. 193.Let [A(0,1), B(1,1)] and [C(1,0)] be the mid-points of the sides of a triangle with incent…
  44. 194.Let P(4,4 √3) be a point on the parabola y^2=4 a x and PQ be a focal chord of the parabola…
  45. 195.If the equation of the parabola with vertex V((3)/(2), 3) and the directrix x+2 y=0 is x^2…
  46. 196.Let ABCD be a trapezium whose vertices lie on the parabola y^2=4 x.
  47. 197.Let the focal chord PQ of the parabola y^2=4 x make an angle of 60^ with the positive x ax…
  48. 198.A line passing through the point A(-2,0), touches the parabola P: y^2=x-2 at the point B i…