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Parabola

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  1. 101.Let PQ be a focal chord of the parabola y^2=4x such that it subtends an angle of 2 at the …
  2. 102.An ellipse E:x^2a^2+y^2b^2=1 passes through the vertices of the hyperbola H:x^249-y^264=-1…
  3. 103.The sum of diameters of the circles that touch (i) the parabola 75x^2=64(5y-3) at the poin…
  4. 104.Let P and Q be any points on the curves (x-1)^2+(y+1)^2=1 and y=x^2, respectively.
  5. 105.The equation of a common tangent to the parabolas y=x^2 and y=-(x-2)^2 is
  6. 106.If the length of the latus rectum of a parabola, whose focus is (a,a) and the tangent at i…
  7. 107.The locus of the mid-point of the line segment joining the focus of the parabola y^2=4ax t…
  8. 108.If the three normals drawn to the parabola y^2=2x pass through the point (a,0), a0, then a…
  9. 109.Let C be the locus of the mirror image of a point on the parabola y^2=4x with respect to t…
  10. 110.Let L be a tangent line to the parabola y^2=4x-20 at (6,2).
  11. 111.Let a parabola P be such that its vertex and focus lie on the positive X-axis at a distanc…
  12. 112.The equation of a circle is Re(z^2)+2[Im(z)]^2+2Re(z)=0 where z=x+iy.
  13. 113.The length of the latus rectum of a parabola, whose vertex and focus are on the positive X…
  14. 114.A tangent and a normal are drawn at the point P(2,-4) on the parabola y^2=8x, which meet t…
  15. 115.The locus of the mid-points of the chords of the hyperbola x^2-y^2=4, which touch the para…
  16. 116.Consider the parabola with vertex (12,34) and directrix y=12.
  17. 117.The locus of a point which divides the line segment joining the point (0,-1) and a point o…
  18. 118.Let L_1 be a tangent to the parabola y^2=4(x+1) and L_2 be a tangent to the parabola y^2=8…
  19. 119.The centre of the circle passing through the point (0,1) and touching the parabola y=x^2 a…
  20. 120.Let the latus rectum of the parabola y^2=4x be the common chord to the circles C_1 and C_2…
  21. 121.The area (in sq.
  22. 122.If the area of the triangle whose one vertex is at the vertex of the parabola y^2+4(x-a^2)…
  23. 123.If the parabolas y^2=4b(x-c) and y^2=8ax have a common normal, then which one of the follo…
  24. 124.The length of the chord of the parabola x^2=4y having equation x-√2y+4√2=0 is:
  25. 125.Axis of a parabola lies along the x-axis.
  26. 126.Let A(4,-4) and B(9,6) be points on the parabola y^2=4x.
  27. 127.The tangents to the curve y=(x-2)^2-1 at its points of intersection with the line x-y=3, i…
  28. 128.The area (in sq.
  29. 129.If one end of a focal chord of the parabola y^2=16x is at (1,4), then the length of this f…
  30. 130.The shortest distance between the line y=x and the curve y^2=x-2 is:
  31. 131.If 5x+9=0 is the directrix of the hyperbola 16x^2-9y^2=144, then its corresponding focus i…
  32. 132.Two parabolas with a common vertex and with axes along the x-axis and y-axis, respectively…
  33. 133.Tangents drawn from the point (-8,0) to the parabola y^2=8x touch the parabola at P and Q.
  34. 134.Let a and b respectively be the semi-transverse and semi-conjugate axes of a hyperbola who…
  35. 135.Let P be the point on the parabola y^2=8x which is at a minimum distance from the centre C…
  36. 136.P and Q are two distinct points on the parabola y^2=4x with parameters t and t_1 respectiv…
  37. 137.Let O be the vertex and Q be any point on the parabola x^2=8y.
  38. 138.The slope of the line touching both the parabolas y^2=4x and x^2=-32y is:
  39. 139.A chord is drawn through the focus of the parabola y^2=6x such that its distance from the …
  40. 140.Let L_1 be the length of the common chord of the curves x^2+y^2=9 and y^2=8x, and let L_2 …
  41. 141.The point of intersection of the normals to the parabola y^2=4x at the ends of its latus r…
  42. 142.The normal at (2,32) to the ellipse x^216+y^23=1 touches a parabola, whose equation is:
  43. 143.If two tangents drawn from a point P to the parabola y^2=4x are at right angles, then the …
  44. 144.A parabola has the origin as its focus and the line x=2 as the directrix.
  45. 145.The equation of a tangent to the parabola y^2=8x is y=x+2.
  46. 146.The locus of the vertices of the family of parabolas y=a^3x^23+a^2x2-2a is:
  47. 147.If a0 and the line 2bx+3cy+4d=0 passes through the points of intersection of the parabolas…
  48. 148.The normal at the point (bt_1^2,2bt_1) on a parabola meets the parabola again at the point…
  49. 149.The normal at the point[( bt_1^2,2bt_1 )] on a parabola meets the parabola again in the po…
  50. 150.Let P be the point (1, 0) and Q a point on the parabola y^2 = 8x.