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Mathematics - Ellipse

Practise 129 JEE Main previous year questions on Ellipse, 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.

Ellipse has been asked in 22 of the 25 years of JEE Main papers analysed (2002–2026), with 129 questions in all. 22% of them were easy, 57% moderate and 22% tough. Most of its questions came from 2025, with 18 questions that year. In the last three years (2024–2026) it had 34 questions across 49 papers, about 0.7 per paper.

The chapter's 12 topics are not weighted equally: Equation of Ellipse (69 questions, 53%), Tangent to ellipse (21 questions, 16%), and Normal to ellipse (13 questions, 10%) have been asked the most. Equation of Ellipse has also led over the last five years, with 39 questions. Equation of Ellipse has produced the most tough questions (15).

  1. 1Let represent an ellipse with major axis along -axis, where is a strictly decreasing positive function on . If the set of all possible value08 Apr, 2026 (E)Equation of Ellipse
  2. 2The eccentricity of an ellipse with centre at the origin is and its directrices are . Let be a hyperbola whose eccentricity is equal to the 06 Apr, 2026 (E)Equation of Ellipse
  3. 3Let be a directrix of an ellipse , whose centre is at the origin and eccentricity is . Let , , be a focus of and be a chord passing through 06 Apr, 2026 (E)Equation of Ellipse
  4. 4Let a focus of the ellipse be and its eccentricity be . If the point lies on and is the origin, then the area of is equal to:05 Apr, 2026 (M)Equation of Ellipse
  5. 5Let an ellipse , , pass through the point and have eccentricity . Then the length of its latus rectum is :02 Apr, 2026 (M)Equation of Ellipse
  6. 6Let A be the point and circles with variable diameter AB touch the circle internally. Let the curve C be the locus of the point B. If the ec02 Apr, 2026 (E)General Equation of 2nd degree curve
  7. 7An ellipse has its center at , one focus at and one vertex at . Then the length of its latus rectum is :28 Jan, 2026 (E)Equation of Ellipse
  8. 8Let the ellipse and the hyperbola have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of 28 Jan, 2026 (E)Equation of Ellipse
  9. 9Let each of the two ellipses and have eccentricity . Let the lengths of the latus recta of and be and , respectively, such that . If the dis24 Jan, 2026 (M)Equation of Ellipse
  10. 10Let the length of the latus rectum of an ellipse , be 30. If its eccentricity is the maximum value of the function , then ( ) is equal to24 Jan, 2026 (E)Equation of Ellipse
  11. 11Let lie on the circle and the point lie on an ellipse with eccentricity . Then the value of is equal to .24 Jan, 2026 (E)Equation of Ellipse
  12. 12Let the line intersect the ellipse at the points A and B. Then the angle made by the line segment AB at the center of the ellipse is :23 Jan, 2026 (M)Equation of Ellipse
  13. 13Let S and be the foci of the ellipse and be a point on the ellipse in the first quadrant. If , then is equal to :22 Jan, 2026 (E)Equation of Ellipse
  14. 14If the line , where , touches the ellipse at the point P in the first quadrant, then one of the focal distances of is :21 Jan, 2026 (E)Equation of Ellipse
  15. 15Let the ellipse pass through the centre of the circle of radius . Let be the focal distances of the point C on the ellipse. Then is equal to08 Apr, 2025 (E)Equation of Ellipse
  16. 16Let and07 Apr, 2025 (E)Equation of Ellipse
  17. 17Let the length of a latus rectum of an ellipse be 10 . If its eccentricity is the minimum value of the function , , then is equal to :07 Apr, 2025 (E)Equation of Ellipse
  18. 18The length of the latus-rectum of the ellipse, whose foci are and and eccentricity is , is04 Apr, 2025 (M)Equation of Ellipse
  19. 19Let C be the circle and be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the stra04 Apr, 2025 (M)Tangent to ellipse
  20. 20The centre of a circle C is at the centre of the ellipse . Let pass through the foci and of such that the circle and the ellipse intersect a04 Apr, 2025 (E)Equation of Ellipse
  21. 21Let for two distinct values of the lines touch the ellipse at the points A and B . Let the line intersect E at the points C and . Then the a04 Apr, 2025 (E)Line and ellipse
  22. 22A line passing through the point intersects the ellipse at and such that is maximum. Then is equal to :03 Apr, 2025 (M)Equation of Ellipse
  23. 23Let be the circle of minimum area enclosing the ellipse with eccentricity and foci . Let PQR be a variable triangle, whose vertex is on the 03 Apr, 2025 (E)Equation of Ellipse
  24. 24If and are the foci of the ellipse and P be a point on the ellipse, then is equal to :02 Apr, 2025 (M)Equation of Ellipse
  25. 25If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse 02 Apr, 2025 (E)Equation of Ellipse
  26. 26Let the ellipse \( {E}_1: {x^2}{ {a}^2}+ {y^2}{ {~b}^2}=1, {a} {b}\) and \( {E}_2: {x^2}{ {~A}^2}+ {y^2}{ {~B}^2}=1, {~A} {B}\) have same ec29 Jan, 2025 (M)Equation of Ellipse
  27. 27If is the equation of the chord of the ellipse , whose mid point is , then is equal to :29 Jan, 2025 (E)Chord with given Middle Point
  28. 28Let be an ellipse. Ellipses 's are constructed such that their centres and eccentricities are same as that of , and the length of minor axis28 Jan, 2025 (M)Equation of Ellipse
  29. 29If the midpoint of a chord of the ellipse is , and the length of the chord is , then is :28 Jan, 2025 (E)Chord with given Middle Point
  30. 30Let the product of the focal distances of the point on the ellipse , be . Then the absolute difference of the eccentricities of two such ell24 Jan, 2025 (M)Equation of Ellipse
  31. 31The equation of the chord, of the ellipse , whose mid-point is is :24 Jan, 2025 (E)Chord with given Middle Point
  32. 32The length of the chord of the ellipse , whose mid-point is , is :23 Jan, 2025 (E)Chord with given Middle Point
  33. 33Let and . If and denote the eccentricity and the length of the latus rectum of the ellipse , then is equal to.09 Apr, 2024 (M)Equation of Ellipse
  34. 34Let the line , intersect the -axis and -axis at the points and , respectively. If the equation of the circle having the line segment as a di05 Apr, 2024 (M)Equation of Ellipse
  35. 35Let P be a point on the ellipse x 2 9 + y 2 4 = 1 . Let the line passing through P and parallel to y - axis meet the circle x 2 + y 2 = 9 at01 Feb, 2024 (E)Equation of Ellipse
  36. 36Let P be a parabola with vertex 2 , 3 and directrix 2 x + y = 6 . Let an ellipse E : x 2 a 2 + y 2 b 2 = 1 , a b of eccentricity 1 2 pass th31 Jan, 2024 (E)Equation of Ellipse
  37. 37If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :30 Jan, 2024 (M)Equation of Ellipse
  38. 38Let A ( α , 0 ) and B ( 0 , β ) be the points on the line 5 x + 7 y = 50 . Let the point P divide the line segment A B internally in the rat30 Jan, 2024 (E)Equation of Ellipse
  39. 39If the points of intersection of two distinct conics x 2 + y 2 = 4 b and x 2 16 + y 2 b 2 = 1 lie on the curve y 2 = 3 x 2 , then 3 3 times 29 Jan, 2024 (M)Equation of Ellipse
  40. 40The length of the chord of the ellipse x 2 25 + y 2 16 = 1 , whose mid point is 1 , 2 5 , is equal to:27 Jan, 2024 (M)Chord with given Middle Point
  41. 41Let an ellipse with centre 1 , 0 and latus rectum of length 1 2 have its major axis along x-axis. If its minor axis subtends an angle 60 at 15 Apr, 2023 (M)Equation of Ellipse
  42. 42Let the tangent and normal at the point 3 3 , 1 on the ellipse x 2 36 + y 2 4 = 1 meet the y - axis at the points A and B respectively. Let 13 Apr, 2023 (M)Normal to ellipse
  43. 43Let P 2 3 7 , 6 7 , Q , R and S be four points on the ellipse 9 x 2 + 4 y 2 = 36 . Let P Q and R S be mutually perpendicular and pass throug12 Apr, 2023 (M)Equation of Ellipse
  44. 44If the radius of the largest circle with centre ( 2 , 0 ) inscribed in the ellipse x 2 + 4 y 2 = 36 is r , then 12 r 2 is equal to11 Apr, 2023 (E)Normal to ellipse
  45. 45Let the ellipse E : x 2 + 9 y 2 = 9 intersect the positive x - and y -axes at the points A and B respectively. Let the major axis of E be a 10 Apr, 2023 (M)Auxillary Circle
  46. 46Let a circle of radius 4 be concentric to the ellipse 15 x 2 + 19 y 2 = 285 . Then the common tangents are inclined to the minor axis of the10 Apr, 2023 (E)Common Tangent
  47. 47The line x = 8 is the directrix of the ellipse E : x 2 a 2 + y 2 b 2 = 1 with the corresponding focus 2 , 0 . If the tangent to E at the poi01 Feb, 2023 (E)Tangent to ellipse
  48. 48If the tangent at a point P on the parabola y 2 = 3 x is parallel to the line x + 2 y = 1 and the tangents at the points Q and R on the elli29 Jan, 2023 (E)Tangent to ellipse
  49. 49Let a tangent to the curve 9 x 2 + 16 y 2 = 144 intersect the coordinate axes at the points A and B . Then, the minimum length of the line s24 Jan, 2023 (M)Tangent to ellipse
  50. 50Let C be the largest circle centred at 2 , 0 and inscribed in the ellipse x 2 36 + y 2 16 = 1 . If 1 , lies on C , then 10 2 is equal to ___24 Jan, 2023 (M)Normal to ellipse

Frequently Asked Questions

1.How many questions are available for Ellipse?

This chapter includes 129 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 Ellipse chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

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

Ellipse has appeared in 22 of the 25 years of JEE Main papers covered here, with 129 questions across 118 papers - about one per paper it appears in.

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

Of the 129 questions analysed for this chapter, 22% are easy, 57% moderate and 22% tough. 2025 had the most, with 18 questions.

5.Which topics in Ellipse should I focus on?

These topics have carried the most weightage in Ellipse:

  • Equation of Ellipse - 69 questions (53%)
  • Tangent to ellipse - 21 questions (16%)
  • Normal to ellipse - 13 questions (10%)
  • Equation of Ellipse has produced the most tough questions (15).
6.Is Ellipse's weightage in JEE Main going up or down?

Across all 118 papers analysed, Ellipse 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.