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Mathematics - Parabola

Practise 149 JEE Main previous year questions on Parabola, compiled from papers spanning 2003 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Parabola has been asked in 22 of the 25 years of JEE Main papers analysed (2002–2026), with 149 questions in all. 14% of them were easy, 60% moderate and 26% tough. Most of its questions came from 2022, with 19 questions that year. In the last three years (2024–2026) it had 36 questions across 49 papers, about 0.7 per paper.

The chapter's 12 topics are not weighted equally: standard equation of parabola (38 questions, 26%), Tangent to Parabola (33 questions, 22%), and Chord of parabola (19 questions, 13%) have been asked the most. standard equation of parabola has also led over the last five years, with 25 questions. Tangent to Parabola has produced the most tough questions (12).

  1. 1Let O be the vertex of the parabola and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segm08 Apr, 2026 (E)Locus
  2. 2Let chord PQ of length of the parabola be such that the ordinates of points and are in the ratio . If the chord PQ subtends an angle at the 06 Apr, 2026 (M)Chord of parabola
  3. 3Let the point be the vertex of the parabola . If a line passing through the point intersects the circle at the points and , then the maximum05 Apr, 2026 (E)standard equation of parabola
  4. 4Let the directrix of the parabola , cut -axis at the point . Let , , be a point on such that the slope of is . If is a focal chord of , then05 Apr, 2026 (E)standard equation of parabola
  5. 5Consider the parabola and the ellipse . Let the line segment joining the points of intersection of and , be their latus rectums. If the ecce04 Apr, 2026 (M)standard equation of parabola
  6. 6Let and be the vertices of a variable right angled triangle inscribed in the parabola . Let the vertex containing the right angle be and the04 Apr, 2026 (E)standard equation of parabola
  7. 7Let the parabola passing through the point be such that the distance between its vertex and the -axis is minimum. Then the value of is:02 Apr, 2026 (E)standard equation of parabola
  8. 8Let A be the focus of the parabola . Let the line intersect the parabola at two distinct points and . If the centroid of the triangle is , t28 Jan, 2026 (E)Chord of parabola
  9. 9Let the image of parabola , in the line be , . Then is equal to24 Jan, 2026 (E)Locus
  10. 10An equilateral triangle OAB is inscribed in the parabola with the vertex O at the vertex of the parabola. Then the minimum distance of the c23 Jan, 2026 (E)Locus
  11. 11If the chord joining the points and on the parabola subtends a right angle at the vertex of the parabola, then is equal to22 Jan, 2026 (M)Chord of parabola
  12. 12Let the locus of the mid-point of the chord through the origin O of the parabola be the curve S. Let P be any point on S. Then the locus of 22 Jan, 2026 (E)Locus
  13. 13Let O be the vertex of the parabola and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in 21 Jan, 2026 (M)Chord with given Middle Point
  14. 14Let be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the -axis such that . Then the locus of the c21 Jan, 2026 (E)Locus
  15. 15Let one end of a focal chord of the parabola be . If divides this focal chord internally in the ratio , then the minimum value of is equal t21 Jan, 2026 (E)Chord of parabola
  16. 16Let be the radius of the circle, which touches x -axis at point and the parabola at the point . Then is equal to ________08 Apr, 2025 (E)Tangent to Parabola
  17. 17Let P be the parabola, whose focus is and directrix is . Then the sum of the ordinates of the points on P , whose abscissa is -2 , is07 Apr, 2025 (M)standard equation of parabola
  18. 18The axis of a parabola is the line and its vertex and focus are in the first quadrant at distances and units from the origin, respectively. 04 Apr, 2025 (E)standard equation of parabola
  19. 19A line passing through the point , touches the parabola at the point in the first quadrant. The area, of the region bounded by the line AB ,04 Apr, 2025 (E)Tangent to Parabola
  20. 20The radius of the smallest circle which touches the parabolas and is03 Apr, 2025 (M)Tangent to Parabola
  21. 21Let the focal chord of the parabola make an angle of with the positive -axis, where P lies in the first quadrant. If the circle, whose one d02 Apr, 2025 (M)Chord of parabola
  22. 22Let the point of the focal chord of the parabola be . If the focus of the parabola divides the chord PQ in the ratio , , then is equal to :02 Apr, 2025 (E)Chord of parabola
  23. 23Two parabolas have the same focus \((4,3)\) and their directrices are the \(x\)-axis and the \(y\)-axis, respectively. If these parabolas in29 Jan, 2025 (M)standard equation of parabola
  24. 24Let be the parabola and be its focus. Let PQ be a focal chord of the parabola such that . Let C be the circle described taking PQ as a diame29 Jan, 2025 (E)Chord of parabola
  25. 25Let be a trapezium whose vertices lie on the parabola . Let the sides and of the trapezium be parallel to y -axis. If the diagonal AC is of 28 Jan, 2025 (M)Chord of parabola
  26. 26Let A and B be the two points of intersection of the line and the mirror image of the parabola with respect to the line . If d denotes the d28 Jan, 2025 (E)standard equation of parabola
  27. 27If the equation of the parabola with vertex and the directrix is , then is equal to :24 Jan, 2025 (E)General Equation of 2nd degree curve
  28. 28If the line intersects the parabola at the points and , then at the vertex of the parabola, the line segment subtends an angle equal to23 Jan, 2025 (M)Chord of parabola
  29. 29Let the shortest distance from , to the parabola be 4 . Then the equation of the circle passing through the point and the focus of the parab23 Jan, 2025 (E)standard equation of parabola
  30. 30The focus of the parabola is the centre of the circle of radius 5 . If the values of , for which C passes through the point of intersection 23 Jan, 2025 (E)standard equation of parabola
  31. 31Let the parabola , meet the coordinate axes at the points and R . If the circle C with centre at passes through the points and , then the ar22 Jan, 2025 (M)standard equation of parabola
  32. 32Let be a point on the parabola and PQ be a focal chord of the parabola. If M and are the foot of perpendiculars drawn from and respectively 22 Jan, 2025 (E)Chord of parabola
  33. 33Let and be three points on the parabola and let the line segment meet the line through parallel to the -axis at the point . Let and respecti09 Apr, 2024 (E)standard equation of parabola
  34. 34Consider the circle and the parabola . If the set of all values of , for which three chords of the circle on three distinct lines passing th09 Apr, 2024 (E)Chord of Contact
  35. 35Let a conic pass through the point and , be any point on . Let the slope of the line touching the conic only at a single point be half the s06 Apr, 2024 (M)standard equation of parabola
  36. 36Let be the lines passing through the point and touching the parabola . Let and be the points on the lines and such that the is an isosceles 06 Apr, 2024 (M)Tangent to Parabola
  37. 37Suppose is a focal chord of the parabola of length and slope . If the distance of the chord from the origin is , then is equal to _______05 Apr, 2024 (M)standard equation of parabola
  38. 38Let a line perpendicular to the line touch the parabola at the point . The distance of the point from the centre of the circle is __________05 Apr, 2024 (E)Line and parabola
  39. 39Let the length of the focal chord PQ of the parabola be 15 units. If the distance of from the origin is , then is equal to _______04 Apr, 2024 (M)standard equation of parabola
  40. 40Let PQ be a chord of the parabola and the midpoint of PQ be at . Then, which of the following point lies on the line passing through the poi04 Apr, 2024 (E)standard equation of parabola
  41. 41The maximum area of a triangle whose one vertex is at ( 0 , 0 ) and the other two vertices lie on the curve y = - 2 x 2 + 54 at points ( x ,30 Jan, 2024 (M)standard equation of parabola
  42. 42Let P ( α , β ) be a point on the parabola y 2 = 4 x . If P also lies on the chord of the parabola x 2 = 8 y whose mid point is 1 , 5 4 , th29 Jan, 2024 (E)Chord with given Middle Point
  43. 43If the shortest distance of the parabola y 2 = 4 x from the centre of the circle x 2 + y 2 - 4 x - 16 y + 64 = 0 is d , then d 2 is equal to27 Jan, 2024 (M)standard equation of parabola
  44. 44Let P Q be a focal chord of the parabola y 2 = 36 x of length 100 , making an acute angle with the positive x - axis. Let the ordinate of P 13 Apr, 2023 (M)Chord of parabola
  45. 45Let a common tangent to the curves y 2 = 4 x and x - 4 2 + y 2 = 16 touch the curves at the points P and Q . Then P Q 2 is equal to ________10 Apr, 2023 (M)Common Tangent
  46. 46Let R be the focus of the parabola y 2 = 20 x and the line y = m x + c intersect the parabola at two points P and Q . Let the points G 10 , 08 Apr, 2023 (M)Chord of parabola
  47. 47The ordinates of the points and on the parabola with focus ( 3 , 0 ) and directrix x = - 3 are in the ratio 3 : 1 . If R ( , ) is the point 08 Apr, 2023 (E)Pair of Tangents
  48. 48If the x -intercept of a focal chord of the parabola y 2 = 8 x + 4 y + 4 is 3 , then the length of this chord is equal to _____ .01 Feb, 2023 (E)Chord of parabola
  49. 49Let S be the set of all a N such that the area of the triangle formed by the tangent at the point P b , c , b , c N , on the parabola y 2 = 31 Jan, 2023 (E)Tangent to Parabola
  50. 50If P ( h , k ) be point on the parabola x = 4 y 2 , which is nearest to the point Q ( 0 , 33 ) , then the distance of P from the directrix o30 Jan, 2023 (M)Normal to Parabola

Frequently Asked Questions

1.How many questions are available for Parabola?

This chapter includes 149 questions compiled from JEE Main papers spanning 2003 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

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

3.Is Parabola an important chapter for JEE Main Mathematics?

Parabola has appeared in 22 of the 25 years of JEE Main papers covered here, with 149 questions across 131 papers - about one per paper it appears in.

4.What is the difficulty level of Parabola questions in JEE Main?

Of the 149 questions analysed for this chapter, 14% are easy, 60% moderate and 26% tough. 2022 had the most, with 19 questions.

5.Which topics in Parabola should I focus on?

These topics have carried the most weightage in Parabola:

  • standard equation of parabola - 38 questions (26%)
  • Tangent to Parabola - 33 questions (22%)
  • Chord of parabola - 19 questions (13%)
  • Tangent to Parabola has produced the most tough questions (12).
6.Is Parabola's weightage in JEE Main going up or down?

Across all 131 papers analysed, Parabola has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.