Jump to a section

Mathematics - Ellipse

Practise 132 AP EAMCET previous year questions on Ellipse, compiled from papers spanning 2001 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty AP EAMCET tests.

Ellipse has been asked in 23 of the 24 years of AP EAMCET papers analysed (2001–2024), with 132 questions in all. 45% of them were easy, 40% moderate and 14% tough. Most of its questions came from 2020, with 17 questions that year. In the last three years (2022–2024) it had 32 questions across 28 papers, about 1.1 per paper.

The chapter's 14 topics are not weighted equally: Equation of Ellipse (48 questions, 36%), Tangent to ellipse (23 questions, 17%), and Line and ellipse (11 questions, 8%) have been asked the most. Equation of Ellipse has also led over the last five years, with 17 questions. Tangent to ellipse has produced the most tough questions (5).

  1. 1Assertion (A) : The length of the latus rectum of an ellipse is 4. The focus and its corresponding directrix are respectively and . Then its27 May, 2025 (M)Equation of Ellipse
  2. 2If the normal drawn at the point on the ellipse meets the ellipse again at , then26 May, 2025 (M)Normal to ellipse
  3. 3If a tangent having slope to the ellipse is a normal to the circle , then lies in the interval26 May, 2025 (E)Tangent to ellipse
  4. 4If is a point on the curve in the first quadrant and the minimum area of the triangle formed by the tangent of the curve at with the coordin26 May, 2025 (E)Tangent to ellipse
  5. 5The area (in sq. units) of the triangle formed by the tangent and normal to the ellipse at the point with the -axis is24 May, 2025 (M)Tangent to ellipse
  6. 6If the tangents drawn from a point to the ellipse are perpendicular, then the locus of is23 May, 2025 (M)Director Circle
  7. 7The equation of the normal drawn at the point to the ellipse is23 May, 2025 (E)Normal to ellipse
  8. 8The angle between the tangents drawn from a point to the ellipse is22 May, 2025 (M)Tangent to ellipse
  9. 9Let be the area of the given ellipse . Let be the area of the region bounded by the curve which is the locus of mid point of the line segmen22 May, 2025 (E)Locus
  10. 10If tangents are drawn to the ellipse , then the locus of the midpoints of the intercepts made by the tangents between the coordinate axes is21 May, 2025 (M)Tangent to ellipse
  11. 11The equation of a chord of an ellipse is . If 0 is the origin, then21 May, 2025 (E)Line and ellipse
  12. 12The square of the slope of a common tangent drawn to the circle and the ellipse is21 May, 2025 (E)Tangent to ellipse
  13. 13Let be the tangent drawn at a point on the ellipse . If is the point where intersects another tangent to the ellipse perpendicularly, then23 May, 2024 (M)Tangent to ellipse
  14. 14If the ellipse is confocal with a hyperbola whose length of the transverse axis is 2 , then the points of intersection of the ellipse and hy22 May, 2024 (M)Locus
  15. 15The length of the latus rectum of is22 May, 2024 (E)Equation of Ellipse
  16. 16If are the areas of ellipse its director circle and auxiliary circle respectively, then21 May, 2024 (M)Director Circle
  17. 17'The product of perpendiculars from the two foci of the ellipse on the tangent at any point on the ellipse is21 May, 2024 (E)Tangent to ellipse
  18. 18Let F and be the foci of the ellipse and is one end of the minor axis. If the area of the triangle is sq. units, then the eccentricity of th20 May, 2024 (M)Equation of Ellipse
  19. 19If the chord of the ellipse having as its middle point is , then20 May, 2024 (E)Chord of ellipse
  20. 20If a tangent of slope 2 to the ellipse touches the circle , then maximum value of is19 May, 2024 (E)Line and ellipse
  21. 21If is a normal to the ellipse , then the equation of the tangent drawn to this ellipse at the point is18 May, 2024 (M)Tangent to ellipse
  22. 22If the lines joining the origin to the points of intersection of and are at right angles, then19 May, 2023 (M)Pair of Tangents
  23. 23Tangents are drawn from point to the ellipse . If are the slopes of these tangents, then with respect to the given ellipse the point19 May, 2023 (M)Pair of Tangents
  24. 24Let be the end points of major axis, be the foci and be the end points of minor axis of an ellipse . If , then18 May, 2023 (M)Chord of ellipse
  25. 25Let the eccentricity of the ellipse be . If the major axis of this ellipse is parallel to Y-axis, then the equation of the tangent to this e18 May, 2023 (E)Tangent to ellipse
  26. 26Let be an ellipse whose major axis is -axis and minor axis is -axis. If the distance of a point on from its foci are and , then the eccentri17 May, 2023 (M)Position of point
  27. 27Let the point L lying in the first quadrant be one end of a latus rectum of the ellipse . Let and be the points where the normal drawn at to17 May, 2023 (E)Tangent to ellipse
  28. 28Let - axis be the transverse axis and - axis be the conjugate axis of a hyperbola . Let the eccentricity of be the reciprocal of the eccentr17 May, 2023 (E)Equation of Ellipse
  29. 29If a normal drawn to the ellipse touches the hyperbola , then the square of the slope of that normal is17 May, 2023 (E)Common Tangent
  30. 30Let and be the foci of an eflipse such that for any point on the ellipse. If and are the end points of the major axis of this ellipse, then16 May, 2023 (M)Equation of Ellipse
  31. 31If a focal chord of the ellipse meets its minor axis at the point , then the perpendicular distance from the centre of the ellipse to this f16 May, 2023 (E)Equation of Ellipse
  32. 32Let be the director circle of an ellipse whose major axis is -axis and minor axis is -axis. If the length of the latus rectum of is 2 , then15 May, 2023 (M)Director Circle
  33. 33Let the length of the latus rectum of an ellipse be equal to the length of its semi-major axis. If the radius of its director circle is and 15 May, 2023 (E)Director Circle
  34. 34Let and be two ellipses and be a rectangle with sides parallel to the coordinate axes. Let be inscribed ellipse in and be circumscribed elli08 Jul, 2022 (M)Equation of Ellipse
  35. 35For belonging to an interval of length , suppose is an interior point of the ellipse . Then,08 Jul, 2022 (E)Position of point
  36. 36The least intercept made by a tangent to the ellipse with coordinate axes is08 Jul, 2022 (E)Tangent to ellipse
  37. 37An ellipse has 6 and 2 as length of major and minor axes respectively. If the centre is at and the major axis is along , then the ellipse is07 Jul, 2022 (M)Equation of Ellipse
  38. 38The foci of the ellipse are07 Jul, 2022 (E)Equation of Ellipse
  39. 39If the latus rectum of an ellipse is equal to half of minor axis, then its eccentricity is06 Jul, 2022 (M)Equation of Ellipse
  40. 40The values of , for which lies inside the ellipse and outside the parabola , satisfy06 Jul, 2022 (E)Position of point
  41. 41If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse is , then it eccentricity is05 Jul, 2022 (M)Equation of Ellipse
  42. 42The distance between the directrices of the ellipse is05 Jul, 2022 (E)Equation of Ellipse
  43. 43The eccentric angle of a point on the ellipse x 2 + 3 y 2 = 6 lying at a distance of 2 units from its centre is04 Jul, 2022 (M)Equation of Ellipse
  44. 44The focal distances of the point 4 5 , 3 5 on the ellipse x 2 4 + y 2 9 = 1 are04 Jul, 2022 (E)Equation of Ellipse
  45. 45The center of ellipse is25 Aug, 2021 (M)General Equation of 2nd degree curve
  46. 46The equation of an ellipse in its standard form, given the distance between its foci is 2 units and the length of its latusrectum is units, 25 Aug, 2021 (E)Equation of Ellipse
  47. 47Find the equation of the ellipse which passes through the points and , whose center lies at and major axis lies along the -axis.24 Aug, 2021 (M)Equation of Ellipse
  48. 48If the lines and are conjugate with respect to the ellipse , then equals24 Aug, 2021 (E)Line and ellipse
  49. 49The sum of the squares of the distances of a moving point from 2 fixed points and is equal to a constant , then the equation of its locus is23 Aug, 2021 (M)Locus
  50. 50The point with respect to the ellipse lies23 Aug, 2021 (M)Position of point

Frequently Asked Questions

1.How many questions are available for Ellipse?

This chapter includes 132 questions compiled from AP EAMCET papers spanning 2001 to 2025.

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

These are AP EAMCET 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 AP EAMCET Mathematics?

Ellipse has appeared in 24 of the 25 years of AP EAMCET papers covered here, with 132 questions across 89 papers - about one per paper it appears in.

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

Of the 132 questions analysed for this chapter, 45% are easy, 40% moderate and 14% tough. 2020 had the most, with 17 questions.

5.Which topics in Ellipse should I focus on?

These topics have carried the most weightage in Ellipse:

  • Equation of Ellipse - 48 questions (36%)
  • Tangent to ellipse - 23 questions (17%)
  • Line and ellipse - 11 questions (8%)
  • Tangent to ellipse has produced the most tough questions (5).
6.Is Ellipse's weightage in AP EAMCET going up or down?

Across all 89 papers analysed, Ellipse has averaged about 1.5 questions per paper. In the last three years (2022–2024), that average has fallen, at about 1.1 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.