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Mathematics - Ellipse

Practise 53 NTA Abhyas (JEE Main) questions on Ellipse. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Ellipse has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 53 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1Let from a point A h , k chords of contact are drawn to the ellipse x 2 + 2 y 2 = 6 where all these chords touch the ellipse x 2 + 4 y 2 = 4
  2. 2If the line x - 2 y = 12 is a tangent to the ellipse x 2 a 2 + y 2 b 2 = 1 at the point 3 , - 9 2 , then the length of the latus rectum of t
  3. 3The line 2 x + y = 3 cuts the ellipse 4 x 2 + y 2 = 5 at points P and Q . If θ is the acute angle between the normals at P and Q , then θ is
  4. 4If the normal to the ellipse x 2 25 + y 2 1 = 1 is at a distance p from the origin, then the maximum value of p is
  5. 5If 0,3 + 5 is a point on the ellipse whose foci are 2,3 and - 2,3 , then the length of the semi-major axis is
  6. 6A normal is drawn to the ellipse x 2 9 + y 2 = 1 at the point 3 cos , sin where 0 2 . If N is the foot of the perpendicular from the origin
  7. 7The tangents at the extremities of the latus rectum of the ellipse 3 x 2 + 4 y 2 = 12 form a rhombus P Q R S . Area (in sq. units) of the rh
  8. 8A tangent having slope - 4 3 to the ellipse x 2 18 + y 2 32 = 1 intersects the major and minor axes at A and B . If O is the origin, then th
  9. 9If the tangent to the ellipse x 2 + 4 y 2 = 16 at P 4 cos ⁡ θ , 2 sin ⁡ θ is also a normal to the circle x 2 + y 2 = 8 x + 4 y , then the su
  10. 10The angle between the pair of tangents drawn to the ellipse 3 x 2 + 2 y 2 = 5 from the point 1 , 2 is tan − 1 12 λ , then the value of λ is
  11. 11The ellipse E 1 : x 2 9 + y 2 4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E 2 passi
  12. 12Let the line y = m x and the ellipse 2 x 2 + y 2 = 1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets
  13. 13The point on the ellipse x 2 6 + y 2 3 = 1 which is nearest to the line x + y = 7 is
  14. 14The focus and corresponding directrix of an ellipse are 3,4 and x + y - 1 = 0 respectively. If the eccentricity of the ellipse is 1 2 , then
  15. 15If the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse x 2 40 + y 2 10 = 1 is x 2 + y 2 2 = a x 2 +
  16. 16If m 1 and m 2 are the slopes of the tangents to the ellipse x 2 16 + y 2 9 = 1 which passes through 5,4 , then the value of m 1 + m 2 - m 1
  17. 17If y = x + c touches the ellipse 3 x 2 + 4 y 2 = 12 at the point P , then the value of the length O P (where O is the origin) is equal to
  18. 18If the common tangents of x 2 + y 2 = r 2 and x 2 16 + y 2 9 = 1 form a square, then the area (in sq. units) of the square is
  19. 19Let S and S ′ are the focii of the ellipse x = 3 + 5 cos ⁡ θ , y = - 2 + 4 sin ⁡ θ . If B is one of the ends of one of the latus rectum, the
  20. 20The length of the portion of the common tangent to x 2 + y 2 = 16 and 9 x 2 + 25 y 2 = 225 between the two points of contact is
  21. 21P 1 and P 2 are corresponding points on the ellipse x 2 16 + y 2 9 = 1 and its auxiliary circle respectively. If the normal at P 1 to the el
  22. 22The point, which is at the shortest distance from the line x + y = 7 and lying on an ellipse x 2 + 2 y 2 = 6 , has coordinates ( a , b ) the
  23. 23If a tangent of slope 2 of the ellipse x 2 a 2 + y 2 1 = 1 passes through the point - 2,0 , then the value of a 2 is equal to
  24. 24If a number of ellipses whose major axis is x -axis and the minor axis is y -axis be described having the same length of the major axis as 2
  25. 25If a , b ∈ R satisfy the equation a 2 + 4 b 2 - 4 = 0 , then the minimum value of 2 a + 3 b will be
  26. 26The vertices of the triangle A B C are A 0,0 , B 3 , 0 and C 3 , 4 , where A and C are foci of an ellipse and B lies on the ellipse. If the
  27. 27If eccentricity of the ellipse x 2 a 2 + 1 + y 2 a 2 + 2 = 1 is 1 6 , then the ratio of the length of the latus rectum to the length of the
  28. 28The line 2 x + y = 3 interesects the ellipse 4 x 2 + y 2 = 5 at two points. The point of intersection of the tangents to the ellipse at thes
  29. 29If the circle whose diameter is the major axis of the ellipse x 2 a 2 + y 2 b 2 = 1 a b 0 meets the minor axis at point P and the orthocentr
  30. 30If common tangents of x 2 + y 2 = r 2 and x 2 16 + y 2 9 = 1 forms a square, then the length of diagonal of the square is
  31. 31An ellipse has foci 4,2 , 2,2 and it passes through the point P 2,4 . The eccentricity of the ellipse is
  32. 32If the tangents P Q and P R are drawn from a variable point P to the ellipse x 2 16 + y 2 9 = 1 , such that the fourth point S of the parall
  33. 33A tangent of slope 2 of the ellipse x 2 a 2 + y 2 1 = 1 passes through - 2 , 0 . Then, three times the square of the eccentricity of the ell
  34. 34An equilateral triangle is inscribed in the ellipse whose equation is x 2 + 4 y 2 = 4 . One vertex of the triangle is 0,1 and one altitude i
  35. 35The focal chord of the parabola y 2 = 32 x touches the ellipse x 2 4 2 + y 2 2 2 = 1 in the first quadrant at the point
  36. 36Variable ellipses are drawn with x = - 4 as directrix and the origin as the corresponding focus. The eccentricity of the locus of the extrem
  37. 37The length of the minor axis of the ellipse 5 x - 10 2 + 5 y + 15 2 = 3 x - 4 y + 7 2 4 is
  38. 38Let from a point A h , k chord of contacts are drawn to the ellipse x 2 + 2 y 2 = 6 such that all these chords touch the ellipse x 2 + 4 y 2
  39. 39If any tangent to the ellipse 25 x 2 + 9 y 2 = 225 meets the coordinate axes at A and B such that O A = O B then, the length A B is equal to
  40. 40Let there are exactly two points on the ellipse x 2 a 2 + y 2 b 2 = 1 whose distances from 0,0 are equal to a 2 2 + b 2 . Then, the eccentri
  41. 41If two points are taken on the minor axis of the ellipse x 2 25 + y 2 9 = 1 at the same distance from the centre as the foci, then the sum o
  42. 42The length of the latus rectum of the curve represented by x = 3 cos ⁡ t + sin ⁡ t and y = 4 cos ⁡ t - sin ⁡ t , is
  43. 43Two lines L 1 and L 2 of slope 1 are tangent to y 2 = 4 x and x 2 + 2 y 2 = 4 respectively, such that the distance d units between L 1 and L
  44. 44The tangent to the ellipse x 2 25 + y 2 16 = 1 at point P lying in the first quadrant meets x -axis at Q and y -axis at R . If the length Q
  45. 45Suppose S and S ′ are foci of the ellipse x 2 25 + y 2 16 = 1 . If P is a variable point on the ellipse and if ∆ is the area (in sq. units)
  46. 46If P and Q are points with eccentric angles θ and θ + π 6 on the ellipse x 2 16 + y 2 4 = 1 , then the area (in sq. units) of the triangle O
  47. 47The line 2 x + y = 3 cuts the ellipse 4 x 2 + y 2 = 5 at P and Q . If θ is the acute angle between normal at P and tangent at Q , then θ is
  48. 48From the point P 3,4 pair of tangents P A and P B are drawn to the ellipse x 2 16 + y 2 9 = 1 . If A B intersects y -axis at C and x -axis a
  49. 49If x 2 + y 2 = a 2 and x 2 16 + y 2 9 = 1 intersect at 4 points P , Q , R and S which form a square, then the area (in sq. units) of the squ
  50. 50The product of the slopes of the common tangents of the ellipse x 2 + 4 y 2 = 16 and the parabola y 2 - 4 x - 4 = 0 is

Frequently Asked Questions

1.How many questions are available for Ellipse?

This chapter includes 53 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Ellipse questions in NTA Abhyas (JEE Main)?

Of the 53 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Ellipse should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.