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Mathematics - Parabola

Practise 92 NTA Abhyas (JEE Main) questions on Parabola. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Parabola has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 92 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1The length of the chord y = 3 x - 2 3 intercepted by the parabola y 2 = 4 x - 1 is equal to
  2. 2If three normals are drawn from the point c , 0 to the parabola y 2 = 4 x and two of which are perpendicular, then the value of c is equal t
  3. 3The point of intersection of the tangent to the parabola y 2 = 4 x which also touches x 2 + y 2 = 1 2 is
  4. 4If two parabolas y 2 = 4 a x – k and x 2 = 4 a y – k have only one common point P , then the equation of normal to y 2 = 4 a x – k at P is
  5. 5The normal to the parabola y 2 = 4 x at P 9 , 6 meets the parabola again at Q . If the tangent at Q meets the directrix at R , then the slop
  6. 6Let B and C are the points of intersection of the parabola x = y 2 and the circle y 2 + x - 2 2 = 8 . The perimeter (in units) of the triang
  7. 7The length of the intercept cut by the line 4 x + 4 3 y - 1 = 0 between the curve y 2 = x is equal to
  8. 8The locus of the centre of the circle described on any focal chord of the parabola y 2 = 4 a x as the diameter is
  9. 9Let the normals at points A 4 a , - 4 a and B 9 a , - 6 a on the parabola y 2 = 4 a x meet at the point P . The equation of the normal from
  10. 10The locus of the middle points of the chords of the parabola y 2 = 4 a x , which passes through the origin is
  11. 11If P Q is the focal chord of the parabola y 2 = - x and P is - 4 , 2 , then the ordinate of the point of intersection of the tangents at P a
  12. 12The locus of the point x , y whose distance from the line y = 2 x + 2 is equal to the distance from 2 , 0 , is a parabola with the length of
  13. 13The length of the chord of the parabola x 2 = 4 y having equation x - 2 y + 4 2 = 0 is
  14. 14The ordinates of the points P and Q on the parabola y 2 = 12 x are in the ratio 1 : 2 . The locus of the point of intersection of the normal
  15. 15If two parabolas y 2 = 4 a x - k and x 2 = 4 a y - k have only one common point P, then the coordinates of P are
  16. 16If the equation of the tangent at the point P 3,4 on the parabola whose axis is the x -axis is 3 x - 4 y + 7 = 0, then the distance of the t
  17. 17If the normals at two points x 1 , y 1 and x 2 , y 2 of the parabola y 2 = 4 x meets again on the parabola, where x 1 + x 2 = 8 , then y 1 -
  18. 18Let the tangents to the parabola y 2 = 4 a x drawn from point P have slope m 1 and m 2 . If m 1 m 2 = 2 , then the locus of point P is
  19. 19The distance between the focus and directrix of the parabola 3 x - y 2 = 48 x + 3 y is
  20. 20Consider a parabola y 2 = 4 x with vertex at A and focus at S . P Q is a chord of the parabola which is normal at point P . If the abscissa
  21. 21Tangents are drawn from any point on the directrix of y 2 = 16 x to the parabola. If the locus of the midpoint of chords of contact is a par
  22. 22A tangent and a normal are drawn at the point P 8,8 on the parabola y 2 = 8 x which cuts the axis of the parabola at the points A and B resp
  23. 23The line y = 2 x + C is a tangent to the parabola y 2 − 4 y − 8 x = 4 at a point whose abscissa is α , then the ordered pair α , C is
  24. 24Chord joining two distinct points P a , 4 b and Q c , - 16 b (both are variable points) on the parabola y 2 = 16 x always passes through a f
  25. 25Let the tangents at points P and R on the parabola y = x 2 intersects at T . Tangent at point Q (lies in between the points P and R ) on the
  26. 26If the line y = - 7 2 is the directrix of the parabola x 2 - k y + 8 = 0 , then the sum of all the possible values of k is equal to
  27. 27The locus of mid-points of all chords of parabola y 2 = 4 x , for which all circles drawn taking them as diameters passes through the vertex
  28. 28If the line y - 2 = 0 is the directrix of the parabola x 2 - k y + 32 = 0 , k ≠ 0 and the parabola intersects the circle x 2 + y 2 = 8 at tw
  29. 29Let l x - 2 y = 1 intersects the parabola y 2 = 4 a x at points P and Q . If P S and Q S meet the parabola again at R and T respectively (wh
  30. 30Let the tangents P Q and P R are drawn to y 2 = 4 a x from any point P on the line x + 4 a = 0 . The angle subtended by the chord of contact
  31. 31The locus of the trisection point of any arbitrary double ordinate of the parabola x 2 = 4 y , is
  32. 32The number of integral points on the circle, touching the parabola y 2 = 8 x at 2 , 4 and passing through 0 , 4 , are equal to
  33. 33The focus of the conic represented parametrically by the equation y = t 2 + 3 , x = 2 t - 1 is
  34. 34If the normals of the parabola y 2 = 4 x drawn at the end points of its latus rectum are tangents to the circle x - 3 2 + y + 2 2 = r 2 , th
  35. 35The normal to the parabola y 2 = 8 x at the point ( 2 , 4 ) meets the parabola again at the point
  36. 36Let P Q be the focal chord of the parabola y 2 = 4 x . If the center of the circle having P Q as its diameter lies on the line y = 4 5 , the
  37. 37If two tangents drawn from the point P ( h , k ) to the parabola y 2 = 8 x are such that the slope of one of the tangent is 3 times the slop
  38. 38The maximum number of points on the parabola y 2 = 16 x which are equidistant from a variable point P (which lie inside the parabola) are
  39. 39Let l 1 and l 2 be the two lines which are normal to y 2 = 4 x and tangent to x 2 = - 12 y respectively (where, l 1 and l 2 are not the x -a
  40. 40The x -intercept of the common tangent to the parabolas y 2 = 32 x and x 2 = 108 y is
  41. 41Let the radius of the circle touching the parabola y 2 = x at 1,1 and having the directrix of y 2 = x as its normal is equal to k 5 units, t
  42. 42The equation of the tangent to the parabola y 2 = 4 x + 5 which is parallel to the line y = 2 x + 7 is
  43. 43Two mutually perpendicular tangents of the parabola y 2 = 4 a x at the points Q 1 and Q 2 on it meet its axis in P 1 and P 2 . If S is the f
  44. 44Let A B is the focal chord of a parabola and D and C be the foot of the perpendiculars from A and B on its directrix respectively. If C D =
  45. 45Tangents to the parabola y 2 = 4 a x at P a t 1 2 , 2 a t 1 and Q a t 2 2 , 2 a t 2 meet at T . If △ P T Q is right-angled at T , then 1 P S
  46. 46The set of points on the axis of the parabola y 2 - 2 y - 4 x + 5 = 0 from which all the three normals drawn to the parabola are real and di
  47. 47If the line y = x - 1 bisects two chords of the parabola y 2 = 4 b x which are passing through the point b , - 2 b , then the length of the
  48. 48Let the lines l 1 and l 2 be normals to y 2 = 4 x and tangents to x 2 = - 12 y (where l 1 and l 2 are not x -axis). The absolute value of th
  49. 49The parabolas C 1 : y 2 = 4 a x - a and C 2 : y 2 = - 4 a x - k intersect at two distinct points A and B . If the slope of the tangent at A
  50. 50The radius of circle, touching the parabola y 2 = 8 x a t 2,4 and passing through 0,4 , is

Frequently Asked Questions

1.How many questions are available for Parabola?

This chapter includes 92 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Parabola chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Parabola questions in NTA Abhyas (JEE Main)?

Of the 92 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Parabola should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.