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Parabola

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  1. 1.Let O be the vertex of the parabola y^2=4 x and its chords OP and OQ are perpendicular to …
  2. 2.Let one root of the quadratic equation in x : (k^2-15k+27)x^2+9(k-1)x+18=0 be twice the ot…
  3. 3.Let chord PQ of length 3√13 of the parabola y^2=12x be such that the ordinates of points P…
  4. 4.Let the directrix of the parabola P:y^2=8x, cut x-axis at the point A .
  5. 5.Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the dista…
  6. 6.Let A be the focus of the parabola y^2 = 8x.
  7. 7.Let the image of parabola x^2=4y, in the line x-y=1 be (y+a)^2=b(x-c), a,b,c N.
  8. 8.An equilateral triangle OAB is inscribed in the parabola y^2=4 x with the vertex O at the …
  9. 9.Let the locus of the mid-point of the chord through the origin O of the parabola y^2=4 x b…
  10. 10.If the chord joining the points P_1(x_1,y_1) and P_2(x_2,y_2) on the parabola y^2=12x subt…
  11. 11.Let y^2 = 12x be the parabola with its vertex at O.
  12. 12.Let one end of a focal chord of the parabola y^2=16x be (16,16).
  13. 13.Let O be the vertex of the parabola x^2=4 y and Q be any point on it.
  14. 14.Let P be the parabola, whose focus is (-2,1) and directrix is 2 x+y+2=0.
  15. 15.A line passing through the point A(-2,0), touches the parabola P:y^2=x-2 at the point B in…
  16. 16.The axis of a parabola is the line y=x and its vertex and focus are in the first quadrant …
  17. 17.The radius of the smallest circle which touches the parabolas y=x^2+2 and x=y^2+2 is
  18. 18.Let the point P of the focal chord PQ of the parabola y^2=16 x be (1,-4).
  19. 19.Let the focal chord PQ of the parabola y^2=4 x make an angle of 60^ with the positive x ax…
  20. 20.Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-ax…
  21. 21.Let ABCD be a trapezium whose vertices lie on the parabola y^2=4x.
  22. 22.If the equation of the parabola with vertex V((3)/(2),3) and the directrix x+2y=0 is x^2+ …
  23. 23.Let the shortest distance from (a, 0), a>0, to the parabola y^2=4 x be 4 .
  24. 24.If the line 3 x-2 y+12=0 intersects the parabola 4 y=3 x^2 at the points A and B, then at …
  25. 25.Let P(4,4√3) be a point on the parabola y^2=4ax and PQ be a focal chord of the parabola.
  26. 26.Let the parabola y=x^2+px-3, meet the coordinate axes at the points P,Q and R .
  27. 27.Let C be the circle of minimum area touching the parabola y=6-x^2 and the lines [y=√3|x|].
  28. 28.Let P Q be a chord of the parabola y^2=12 x and the midpoint of P Q be at (4,1).
  29. 29.If the shortest distance of the parabola y^2=4 x from the centre of the circle x^2+y^2-4 x…
  30. 30.Let PQ be a focal chord of the parabola y^2=36x of length 100 , making an acute angle with…
  31. 31.Let A(0,1),B(1,1) and C(1,0) be the mid-points of the sides of a triangle with incentre at…
  32. 32.Let R be the focus of the parabola y^2=20 x and the line y=m x+c intersect the parabola at…
  33. 33.Let A be a point on the x-axis.
  34. 34.The parabolas : a x^2+2 b x+c y=0 and d x^2+2 e x+f y=0 intersect on the line y=1.
  35. 35.The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax …
  36. 36.The area (in sq.
  37. 37.Let A,B and C be the vertices of a variable right angled triangle inscribed in the parabol…
  38. 38.Let r be the radius of the circle, which touches x - axis at point (a, 0), a<0 and the par…
  39. 39.Let y^2=12 x be the parabola and S be its focus.
  40. 40.Let A and B be the two points of intersection of the line y+5=0 and the mirror image of th…
  41. 41.The focus of the parabola y^2=4 x+16 is the centre of the circle C of radius 5 .
  42. 42.Let A, B and C be three points on the parabola y^2=6 x and let the line segment A B meet t…
  43. 43.Consider the circle C: x^2+y^2=4 and the parabola P: y^2=8 x.
  44. 44.Let a conic C pass through the point (4,-2) and P(x,y),x 3, be any point on C.
  45. 45.Let L_1, L_2 be the lines passing through the point P(0,1) and touching the parabola 9 x^2…
  46. 46.Let a line perpendicular to the line 2 x-y=10 touch the parabola y^2=4(x-9) at the point P…
  47. 47.Suppose AB is a focal chord of the parabola y^2=12x of length l and slope m<√3.
  48. 48.Let the length of the focal chord PQ of the parabola y^2=12 x be 15 units.
  49. 49.Let the line L:√2x+y= pass through the point of the intersection P (in the first quadrant)…
  50. 50.Let [P(, )] be a point on the parabola y^2=4 x.