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Mathematics - Ellipse

Practise 38 NDA previous year questions on Ellipse, compiled from papers spanning 2010 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 NDA tests.

Ellipse has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 38 questions in all. 47% of them were easy, 53% moderate and 0% tough. Most of its questions came from 2010, with 5 questions that year. In the last three years (2024–2026) it had 5 questions across 5 papers, about 1 per paper.

The chapter's 4 topics are not weighted equally: Equation of Ellipse (33 questions, 87%), General Equation of 2nd degree curve (3 questions, 8%), and Line and ellipse (1 question, 3%) have been asked the most. Equation of Ellipse has also led over the last five years, with 10 questions.

  1. 1Passage: The foci of the ellipse and the foci of the hyperbola coincide (assume p$ ?2026 (Phase 1)Equation of Ellipse
  2. 2Passage: The foci of the ellipse and the foci of the hyperbola coincide (assume $p Question: What is the difference between the eccentriciti2026 (Phase 1)Equation of Ellipse
  3. 3If any point on an ellipse is , then what is the eccentricity of the ellipse?2025 (Phase 1)Equation of Ellipse
  4. 4What is the eccentricity of the ellipse if the angle between the straight lines joining the foci to an extremity of the minor axis is ?2024 (Phase 1)Equation of Ellipse
  5. 5The foci of the ellipse are at Q and R . If is any point on the ellipse, then what is equal to?2024 (Phase 2)Equation of Ellipse
  6. 6Paragraph: Consider the following for the next two (02) items that follow: is any point on the ellipse . Let be the foci of the ellipse. Que2023 (Phase 1)Equation of Ellipse
  7. 7Paragraph: Consider the following for the next two items that follow: is any point on the ellipse . Let be the foci of the ellipse. Question2023 (Phase 1)Equation of Ellipse
  8. 8Given that What is the maximum value of y?2023 (Phase 2)Equation of Ellipse
  9. 9Consider the following in respect of the equation 1. The equation represents an ellipse if . 2. The equation represents a hyperbola if 3. Th2023 (Phase 2)General Equation of 2nd degree curve
  10. 10What is the distance between the foci of the ellipse ?2022 (Phase 1)Equation of Ellipse
  11. 11The centre of an ellipse is at , major axis is on the -axis. If the ellipse passes through and , then what is its eccentricity?2022 (Phase 2)Equation of Ellipse
  12. 12Consider the following with regard to eccentricity of a conic section : 1. for circle 2. for parabola 3. for ellipse Which of the above are 2021 (Phase 1)Equation of Ellipse
  13. 13Let be any point on the ellipse . If and are two points, then what is equal to?2020Equation of Ellipse
  14. 14The sum of the focal distances of a point on an ellipse is constant and equal to the2019 (Phase 1)Equation of Ellipse
  15. 15If the angle between the lines joining the end points of minor axis of the ellipse with one of its foci is , then what is the eccentricity o2019 (Phase 2)Equation of Ellipse
  16. 16What is the equation of the ellipse whose vertices are and foci are at ?2018 (Phase 1)Equation of Ellipse
  17. 17The second degree equation represents2018 (Phase 2)General Equation of 2nd degree curve
  18. 18What is the equation of the ellipse having foci and the eccentricity ?2017 (Phase 1)Equation of Ellipse
  19. 19A man running round a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the 2017 (Phase 2)Equation of Ellipse
  20. 20The position of the point relative to the ellipse is2017 (Phase 2)Position of point
  21. 21The equation of the ellipse whose centre is at origin, major axis is along x -axis with eccentricity and latus rectum 4 units is2017 (Phase 2)Equation of Ellipse
  22. 22If the ellipse intercepts the line , then what is the length of the chord so formed?2016 (Phase 2)Line and ellipse
  23. 23Consider any point P on the ellipse in the first quadrant. Let and represent its distances from and respectively, then is equal to2015 (Phase 2)Equation of Ellipse
  24. 24What is the sum of the major and minor axes of the ellipse whose eccentricity is and length of latus rectum is 14.4 unit?2014 (Phase 1)Equation of Ellipse
  25. 25Paragraph : Consider an ellipse Question : What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse2014 (Phase 1)Equation of Ellipse
  26. 26What is the length of the latus rectum of the ellipse ?2014 (Phase 2)Equation of Ellipse
  27. 27The equation of the ellipse whose vertices are at and foci at is2013 (Phase 1)Equation of Ellipse
  28. 28The length of latus rectum of the ellipse is2013 (Phase 2)Equation of Ellipse
  29. 29If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?2012 (Phase 1)Equation of Ellipse
  30. 30What is the eccentricity of the conic ?2012 (Phase 1)Equation of Ellipse
  31. 31The sum of the focal distances of a point on the ellipse is :2012 (Phase 2)Equation of Ellipse
  32. 32The eccentricity of an ellipse satisfies the condition:2012 (Phase 2)Equation of Ellipse
  33. 33What is the sum of the focal distances of a point of an ellipse ?2011 (Phase 1)Equation of Ellipse
  34. 34If and are the foci of an ellipse and the semi-minor axis is 3 ; then the ellipse passes through which one of the following points?2010 (Phase 1)Equation of Ellipse
  35. 35A circle is drawn with the two foci of an ellipse at the end of the diameter. What is the equation to the circle?2010 (Phase 1)Equation of Ellipse
  36. 36What are the equations of the directrices of the ellipse ?2010 (Phase 1)Equation of Ellipse
  37. 37A point moves such that the difference of its distances from two given points and is constant. What is the locus of the point ?2010 (Phase 2)General Equation of 2nd degree curve
  38. 38If the latus rectum of an ellipse is equal to half its minor axis, then what is its eccentricity?2010 (Phase 2)Equation of Ellipse

Frequently Asked Questions

1.How many questions are available for Ellipse?

This chapter includes 38 questions compiled from NDA papers spanning 2010 to 2026.

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

These are NDA 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 NDA Mathematics?

Ellipse has appeared in 17 of the 17 years of NDA papers covered here, with 38 questions across 27 papers - about one per paper it appears in.

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

Of the 38 questions analysed for this chapter, 47% are easy, 53% moderate and 0% tough. 2010 had the most, with 5 questions.

5.Which topics in Ellipse should I focus on?

These topics have carried the most weightage in Ellipse:

  • Equation of Ellipse - 33 questions (87%)
  • General Equation of 2nd degree curve - 3 questions (8%)
  • Line and ellipse - 1 question (3%)
6.Is Ellipse's weightage in NDA going up or down?

Across all 27 papers analysed, Ellipse has averaged about 1.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.