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Mathematics - Ellipse

Practise 22 JEE Advanced previous year questions on Ellipse, compiled from papers spanning 2007 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 Advanced tests.

Ellipse has been asked in 17 of the 27 years of JEE Advanced papers analysed (2000–2026), with 22 questions in all. 14% of them were easy, 36% moderate and 50% tough. Most of its questions came from 2009, with 3 questions that year. In the last three years (2024–2026) it had 4 questions across 6 papers, about 0.7 per paper.

The chapter's 7 topics are not weighted equally: Equation of Ellipse (8 questions, 36%), Tangent to ellipse (7 questions, 32%), and Auxillary Circle (2 questions, 9%) have been asked the most. Equation of Ellipse has also led over the last five years, with 2 questions. Equation of Ellipse has produced the most tough questions (5).

  1. 1Consider the ellipse given by . Let be the hyperbola whose eccentricity is the reciprocal of the eccentricity of and whose foci are the same2026 (Paper 2)Equation of Ellipse
  2. 2Passage: Consider the ellipses given by and . Question: Let be the point in the first quadrant where the given ellipses intersect. If is the2026 (Paper 2)Tangent to ellipse
  3. 3Let and be two distinct points on the ellipse such that , and . Let C denote the circle , and be the point . Suppose the line intersects at 2025 (Paper 2)Equation of Ellipse
  4. 4Consider the ellipse . Let be a point in the first quadrant such that . Two tangents are drawn from to the ellipse, of which one meets the e2024 (Paper 1)Tangent to ellipse
  5. 5Let T 1 and T 2 be two distinct common tangents to the ellipse E : x 2 6 + y 2 3 = 1 and the parabola P : y 2 = 12 x . Suppose that the tang2023 (Paper 1)Common Tangent
  6. 6Consider the ellipse x 2 4 + y 2 3 = 1 . Let H , 0 , 0 2 , be a point. A straight line drawn through H parallel to the y -axis crosses the e2022 (Paper 1)Auxillary Circle
  7. 7Let E be the ellipse x 2 16 + y 2 9 = 1 . For any three distinct points P , Q and Q on E , let M P , Q be the mid-point of the line segment 2021 (Paper 2)Chord with given Middle Point
  8. 8Define the collections E 1 , E 2 , E 3 , . . . . of ellipses and R 1 , R 2 , R 3 , . . . . of rectangles as follows: E 1 : x 2 9 + y 2 4 = 12019 (Paper 1)Equation of Ellipse
  9. 9Consider two straight lines, each of which is tangent to both the circle x 2 + y 2 = 1 2 and the parabola y 2 = 4 x . Let these lines inters2018 (Paper 2)Equation of Ellipse
  10. 10Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. Column 1 Column 2 Column 3 (I) x2017 (Paper 1)Tangent to ellipse
  11. 11Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. Column 1 Column 2 Column 3 (I) x2017 (Paper 1)Tangent to ellipse
  12. 12Paragraph: Let and , for , be the foci of the ellipse Suppose a parabola having vertex at the origin and focus at intersects the ellipse at 2016 (Paper 2)Chord of Contact
  13. 13Let E 1 and E 2 be two ellipse whose centers are at the origin. The major axes of E 1 a n d E 2 lie along the x - axis and the y - axis, res2015 (Paper 2)Tangent to ellipse
  14. 14A vertical line passing through the point h , 0 intersects the ellipse x 2 4 + y 2 3 = 1 at the points P and Q . Let the tangents to the ell2013 (Paper 1)Tangent to ellipse
  15. 15The ellipse is inscribed in a rectangle whose sides are parallel to the coordinate axes. Another ellipse passing through the point circumscr2012 (Paper 1)Equation of Ellipse
  16. 16Paragraph: Tangents are drawn from the point to the ellipse touching the ellipse at points and . Question: The coordinates of and are2010 (Paper 2)Tangent to ellipse
  17. 17Paragraph: Tangents are drawn from the point to the ellipse touching the ellipse at points and . Question: The equation of the locus of the 2010 (Paper 2)Locus
  18. 18The line passing through the extremity of the major axis and extremity of the minor axis of the ellipse meets its auxiliary circle at the po2009 (Paper 1)Auxillary Circle
  19. 19The normal at a point on the ellipse meets the -axis at . If is the mid-point of the line segment , then the locus of intersects the latusre2009 (Paper 2)Locus
  20. 20An ellipse intersects the hyperbola orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the2009 (Paper 2)Equation of Ellipse
  21. 21Let and , be the end points of the latusrectum of the ellipse . The equations of parabolas with latusrectum are2008 (Paper 1)Equation of Ellipse
  22. 22A hyperbola, having the transverse axis of length , is confocal with the ellipse . Then, its equation is2007 (Paper 1)Equation of Ellipse

Frequently Asked Questions

1.How many questions are available for Ellipse?

This chapter includes 22 questions compiled from JEE Advanced papers spanning 2007 to 2026.

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

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

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

Ellipse has appeared in 17 of the 21 years of JEE Advanced papers covered here, with 22 questions across 18 papers - about one per paper it appears in.

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

Of the 22 questions analysed for this chapter, 14% are easy, 36% moderate and 50% tough. 2009 had the most, with 3 questions.

5.Which topics in Ellipse should I focus on?

These topics have carried the most weightage in Ellipse:

  • Equation of Ellipse - 8 questions (36%)
  • Tangent to ellipse - 7 questions (32%)
  • Auxillary Circle - 2 questions (9%)
  • Equation of Ellipse has produced the most tough questions (5).
6.Is Ellipse's weightage in JEE Advanced going up or down?

Across all 18 papers analysed, Ellipse has averaged about 1.2 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.