Jump to a section

Mathematics - Hyperbola

Practise 107 JEE Main previous year questions on Hyperbola, compiled from papers spanning 2005 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.

Hyperbola has been asked in 16 of the 25 years of JEE Main papers analysed (2002–2026), with 107 questions in all. 21% of them were easy, 56% moderate and 22% tough. Most of its questions came from 2022, with 17 questions that year. In the last three years (2024–2026) it had 31 questions across 49 papers, about 0.6 per paper.

The chapter's 9 topics are not weighted equally: Equation of hyperbola (47 questions, 44%), Tangent to hyperbola (19 questions, 18%), and Normal to hyperbola (14 questions, 13%) have been asked the most. Equation of hyperbola has also led over the last five years, with 36 questions. Equation of hyperbola has produced the most tough questions (10).

  1. 1If the eccentricity of the hyperbola , passing through , satisfies , then the length of the latus rectum of the hyperbola is:06 Apr, 2026 (M)Equation of hyperbola
  2. 2Let the eccentricity of a hyperbola satisfy the equation . If the foci of the hyperbola are and , then the length of its latus rectum is :05 Apr, 2026 (E)Equation of hyperbola
  3. 3Let be a hyperbola such that the distance between its foci is and the distance between its directrices is . If the line intersects the hyper04 Apr, 2026 (E)Equation of hyperbola
  4. 4Let O be the origin, and P and Q be two points on the rectangular hyperbola such that the mid point of the line segment PQ is . Then the are02 Apr, 2026 (E)Chord with given Middle Point
  5. 5For some , let the eccentricity and the length of the latus rectum of the hyperbola be and , respectively, and let the eccentricity and the 28 Jan, 2026 (M)Equation of hyperbola
  6. 6Let the domain of the function be the interval . Let the hyperbola have eccentricity and the length of the latus rectum . Then is equal to :23 Jan, 2026 (M)Equation of hyperbola
  7. 7Let PQ be a chord of the hyperbola , perpendicular to the x -axis such that OPQ is an equilateral triangle, O being the centre of the hyperb23 Jan, 2026 (E)Equation of hyperbola
  8. 8If the line , where , does not meet the hyperbola , then a possible value of is:22 Jan, 2026 (M)Line and hyperbola
  9. 9Let be a point on the hyperbola , whose foci are S and . If the length of its latus rectum is 8, then the square of the area of is equal to 22 Jan, 2026 (E)Equation of hyperbola
  10. 10Let the foci of a hyperbola coincide with the foci of the ellipse . If the eccentricity of the hyperbola is 5, then the length of its latus 21 Jan, 2026 (M)Equation of hyperbola
  11. 11Consider the hyperbola having one of its focus at . If the latus ractum through its other focus subtends a right angle at P and .07 Apr, 2025 (M)Equation of hyperbola
  12. 12Let and be the eccentricities of the ellipse and the hyperbola , respectively. If and , then the eccentricity of the ellipse having its axes07 Apr, 2025 (E)Mixed Questions of Ellipse and Hyperbola
  13. 13Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the corre07 Apr, 2025 (E)Equation of hyperbola
  14. 14Let the sum of the focal distances of the point on the hyperbola be . If for , the length of the latus rectum is and the product of the foca04 Apr, 2025 (E)Equation of hyperbola
  15. 15Let the product of the focal distances of the point on the hyperbola be 32 . Let the length of the conjugate axis of be and the length of it03 Apr, 2025 (M)Equation of hyperbola
  16. 16If the equation of the hyperbola with foci and is , then is equal to _____.03 Apr, 2025 (E)Equation of hyperbola
  17. 17Let one focus of the hyperbola be at and the corresponding directrix be . If e and respectively are the eccentricity and the length of the l02 Apr, 2025 (M)Equation of hyperbola
  18. 18If and are the points of intersection of the circle and the hyperbola and a point P moves on the line , then the centroid of lies on the lin28 Jan, 2025 (E)Locus
  19. 19Let and be two hyperbolas having length of latus rectums and respectively. Let their ecentricities be and respectively. If the product of th24 Jan, 2025 (E)Equation of hyperbola
  20. 20Let the circle touch the line , have the centre on the positive x -axis, and cut off a chord of length along the line . Let H be the hyperbo23 Jan, 2025 (M)Equation of hyperbola
  21. 21Let the foci of a hyperbola be and . If it passes through the point , then the length of its latus-rectum is :22 Jan, 2025 (M)Equation of hyperbola
  22. 22Let and . Let the distance between the foci of E and the foci of be . If , and the ratio of the eccentricities of and is , then the sum of t22 Jan, 2025 (E)Equation of hyperbola
  23. 23Let the foci of a hyperbola coincide with the foci of the ellipse and the eccentricity of the hyperbola be the reciprocal of the eccentricit09 Apr, 2024 (E)Equation of hyperbola
  24. 24Let be the hyperbola, whose eccentricity is and the length of the latus rectum is . Suppose the point lies on . If is the product of the foc08 Apr, 2024 (M)Equation of hyperbola
  25. 25Let be the focus of the hyperbola , on the positive -axis. Let be the circle with its centre at and passing through the point . If is the or08 Apr, 2024 (E)Equation of hyperbola
  26. 26The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and , respectively. Let the line touch this hyperbol06 Apr, 2024 (E)Tangent to hyperbola
  27. 27Let be a square matrix of order 2 such that and the sum of its diagonal elements is -3 . If the points satisfying lie on a hyperbola, whose 04 Apr, 2024 (M)Equation of hyperbola
  28. 28Consider a hyperbola having centre at the origin and foci on the -axis. Let be the circle touching the hyperbola and having the centre at th04 Apr, 2024 (E)Equation of hyperbola
  29. 29Let x 2 a 2 + y 2 b 2 = 1 , a b be an ellipse, whose eccentricity is 1 2 and the length of the latus rectum is 14 . Then the square of the e01 Feb, 2024 (M)Equation of hyperbola
  30. 30For 0 θ π / 2 , if the eccentricity of the hyperbola x 2 − y 2 cosec 2 θ = 5 is 7 times eccentricity of the ellipse x 2 cosec 2 θ + y 2 = 5 01 Feb, 2024 (M)Equation of hyperbola
  31. 31If the foci of a hyperbola are same as that of the ellipse x 2 9 + y 2 25 = 1 and the eccentricity of the hyperbola is 15 8 times the eccent31 Jan, 2024 (M)Equation of hyperbola
  32. 32Let the foci and length of the latus rectum of an ellipse x 2 a 2 + y 2 b 2 = 1 , a b be ± 5 , 0 and 50 , respectively. Then, the square of 31 Jan, 2024 (M)Equation of hyperbola
  33. 33Let the latus rectum of the hyperbola x 2 9 - y 2 b 2 = 1 subtend an angle of π 3 at the centre of the hyperbola. If b 2 is equal to l m ( 130 Jan, 2024 (M)Equation of hyperbola
  34. 34Let P be a point on the hyperbola H : x 2 9 - y 2 4 = 1 , in the first quadrant such that the area of triangle formed by P and the two foci 30 Jan, 2024 (E)Equation of hyperbola
  35. 35Let e 1 be the eccentricity of the hyperbola x 2 16 - y 2 9 = 1 and e 2 be the eccentricity of the ellipse x 2 a 2 + y 2 b 2 = 1 , a b , whi27 Jan, 2024 (E)Equation of hyperbola
  36. 36Let m 1 and m 2 be the slopes of the tangents drawn from the point P 4 , 1 to the hyperbola H : y 2 25 - x 2 16 = 1 If Q is the point from w13 Apr, 2023 (M)Tangent to hyperbola
  37. 37The foci of a hyperbola are ( 2 , 0 ) and its eccentricity is 3 2 . A tangent, perpendicular to the line 2 x + 3 y = 6 , is drawn at a point13 Apr, 2023 (E)Tangent to hyperbola
  38. 38Let H n : x 2 1 + n - y 2 3 + n = 1 , n . Let k be the smallest even value of n such that the eccentricity of H k is a rational number. If l11 Apr, 2023 (M)Equation of hyperbola
  39. 39Let R be a rectangle given by the lines x = 0 , x = 2 , y = 0 and y = 5 . Let A , 0 and B 0 , , 0 , 2 and 0 , 5 , be such that the line segm11 Apr, 2023 (M)Locus
  40. 40Let the tangent to the parabola y 2 = 12 x at the point 3 , be perpendicular to the line 2 x + 2 y = 3 . Then the square of distance of the 11 Apr, 2023 (E)Normal to hyperbola
  41. 41Let the eccentricity of an ellipse x 2 a 2 + y 2 b 2 = 1 is reciprocal to that of the hyperbola 2 x 2 - 2 y 2 = 1 . If the ellipse intersect06 Apr, 2023 (E)Mixed Questions of Ellipse and Hyperbola
  42. 42Let P x 0 , y 0 be the point on the hyperbola 3 x 2 - 4 y 2 = 36 , which is nearest to the line 3 x + 2 y = 1 . Then 2 y 0 - x 0 is equal to01 Feb, 2023 (E)Tangent to hyperbola
  43. 43If the maximum distance of normal to the ellipse x 2 4 + y 2 b 2 = 1 , b 2 , from the origin is 1 , then the eccentricity of the ellipse is:31 Jan, 2023 (M)Normal to hyperbola
  44. 44Let H be the hyperbola, whose foci are 1 2 , 0 and eccentricity is 2 . Then the length of its latus rectum is:31 Jan, 2023 (E)Equation of hyperbola
  45. 45The vertices of a hyperbola H are 6 , 0 and its eccentricity is 5 2 . Let N be the normal to H at a point in the first quadrant and parallel25 Jan, 2023 (M)Normal to hyperbola
  46. 46Let the focal chord of the parabola P : y 2 = 4 x along the line L : y = m x + c , m 0 meet the parabola at the points M and N . Let the lin29 Jul, 2022 (M)Tangent to hyperbola
  47. 47For the hyperbola H : x 2 - y 2 = 1 and the ellipse E : x 2 a 2 + y 2 b 2 = 1 , a b 0 , let the (1) eccentricity of E be reciprocal of the e28 Jul, 2022 (M)Common Tangent
  48. 48Let the hyperbola H : x 2 a 2 - y 2 b 2 = 1 pass through the point 2 2 , - 2 2 . A parabola is drawn whose focus is same as the focus of H w28 Jul, 2022 (E)Equation of hyperbola
  49. 49An ellipse E : x 2 a 2 + y 2 b 2 = 1 passes through the vertices of the hyperbola H : x 2 49 - y 2 64 = - 1 . Let the major and minor axes o27 Jul, 2022 (M)Mixed Questions of Ellipse and Hyperbola
  50. 50A common tangent T to the curves C 1 : x 2 4 + y 2 9 = 1 and C 2 : x 2 42 - y 2 143 = 1 does not pass through the fourth quadrant. If T touc27 Jul, 2022 (E)Common Tangent

Frequently Asked Questions

1.How many questions are available for Hyperbola?

This chapter includes 107 questions compiled from JEE Main papers spanning 2005 to 2026.

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

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

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

Hyperbola has appeared in 16 of the 25 years of JEE Main papers covered here, with 107 questions across 101 papers - about one per paper it appears in.

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

Of the 107 questions analysed for this chapter, 21% are easy, 56% moderate and 22% tough. 2022 had the most, with 17 questions.

5.Which topics in Hyperbola should I focus on?

These topics have carried the most weightage in Hyperbola:

  • Equation of hyperbola - 47 questions (44%)
  • Tangent to hyperbola - 19 questions (18%)
  • Normal to hyperbola - 14 questions (13%)
  • Equation of hyperbola has produced the most tough questions (10).
6.Is Hyperbola's weightage in JEE Main going up or down?

Across all 101 papers analysed, Hyperbola has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.