Jump to a section

Mathematics - Ellipse

Practise 38 WBJEE previous year questions on Ellipse, compiled from papers spanning 2009 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 WBJEE tests.

Ellipse has been asked in 17 of the 18 years of WBJEE papers analysed (2009–2026), with 38 questions in all. 32% of them were easy, 58% moderate and 11% tough. Most of its questions came from 2020, with 4 questions that year. In the last three years (2024–2026) it had 5 questions across 3 papers, about 1.7 per paper.

The chapter's 10 topics are not weighted equally: Equation of Ellipse (12 questions, 32%), Locus (9 questions, 24%), and Tangent to ellipse (6 questions, 16%) have been asked the most. Over the last five years the most frequent topics have been Locus (3), Equation of Ellipse (2), and Tangent to ellipse (2). Locus has produced the most tough questions (3).

  1. 1The minimum length of intercept on any tangent to the ellipse cut by the circle is2026Tangent to ellipse
  2. 2Consider the following ellipse: , where is a positive decreasing function. Then the value (values) of for which the major axis coincides wit2026Equation of Ellipse
  3. 3A line of fixed length moves so that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the l2024Locus
  4. 4With origin as a foucs and x = 4 as corresponding directrix, a family of ellipse are drawn. Then the locus of an end of minor axis is2024Locus
  5. 5In a plane and are the position vectors of two points and respectively. A point with position vector moves on that plane in such a way that 2024General Equation of 2nd degree curve
  6. 6The tangent at point \((a , b ), 0 < < { }{2}\), to the ellipse \( {x^2}{a^2}+ {y^2}{b^2}=1\) meets the \(x\)-axis at \(T\) and \(y\)-axis a2023Tangent to ellipse
  7. 7If the lines joining the focii of the ellipse \( {x^2}{a^2}+ {y^2}{b^2}=1\) where \(a > b\), and an extremity of its minor axis is inclined 2023Equation of Ellipse
  8. 8is a variable chord of the ellipse . If subtends a right angle at the origin , then equals to2022Chord of ellipse
  9. 9Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on2022Locus
  10. 10The co-ordinate of a point on the auxiliary circle of the ellipse corresponding to the point on the ellipse whose eccentric angle is will be2021Auxillary Circle
  11. 11The points of intersection of two ellipses and lie on a circle. The centre of the circle is2021Position of point
  12. 12Area in the first quadrant between the ellipses and is2020Equation of Ellipse
  13. 13If and are the ends of minor axis and and are the foci of the ellipse , then the area of the rhombus will be2020Equation of Ellipse
  14. 14Consider the curve . The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtend2020Tangent to ellipse
  15. 15Consider a tangent to the ellipse at any point. The locus of the midpoint of the portion intercepted between the axes is2020Locus
  16. 16Sand are the foci of an ellipse and is the end point of the minor axis. If is equilateral triangle, the eccentricity of the ellipse is2019Equation of Ellipse
  17. 17is the extremity of the latusrectum of ellipse in the first quadrant. The eccentric angle of is2019Equation of Ellipse
  18. 18Let be a point on the ellipse and the line through parallel to the -axis mects the circle at where are on the same side of the -axis. If is 2018Locus
  19. 19is an extremity of the minor axis of an ellipse whose foci are and If is a right angle, then the eccentricity of the ellipse is2017Position of point
  20. 20Tangents are drawn to the ellipse at the ends of both latusrectum. The area of the quadrilateral, so formed is2017Pair of Tangents
  21. 21The line is tangent to the ellipse Then is2016Properties of Tangent
  22. 22The equation of auxiliary circle of the ellipse is2016Auxillary Circle
  23. 23On the ellipse , the points at which the tangents are parallel to the line are2016Tangent to ellipse
  24. 24Number of intersecting points of the conics and is2015General Equation of 2nd degree curve
  25. 25Let the equation of an ellipse be Then, the radius of the circle with centre and passing through the foci of the ellipse is2014Equation of Ellipse
  26. 26For the variable, the locus of the point of intersection of the lines and is2013Locus
  27. 27The locus of the mid-points of the chords of an ellipse that are drawn from the positive end of the minor axis, is2013Locus
  28. 28The line intersects the hyperbola at the points and The eccentricity of ellipse with as major axis and minor axis of length is2013Locus
  29. 29If the distance between the foci of an ellipse is equal to the length of the latusrectum, then its eccentricity is2013Equation of Ellipse
  30. 30Let the foci of the ellipse subtend a right angle at a point . Then, the locus of is2012Locus
  31. 31The line intersects the ellipse at the points and The equation of the circle with as diameter is2012Line and ellipse
  32. 32The eccentric angle in the first quadrant of a point on the ellipse at a distance 3 units from the centre of the ellipse is2012Equation of Ellipse
  33. 33The length of the latus rectum of the ellipse \(16 x^2+25 y^2=400\) is2011Equation of Ellipse
  34. 34S and are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is2010Equation of Ellipse
  35. 35The line intersects the ellipse in real points if2009Line and ellipse
  36. 36The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is . The eccentricity of the ellips2009Equation of Ellipse
  37. 37The equation of the tangent to the conic at is2009Tangent to ellipse
  38. 38The total number of tangents through the point that can be drawn to the ellipses and is2009Tangent to ellipse

Frequently Asked Questions

1.How many questions are available for Ellipse?

This chapter includes 38 questions compiled from WBJEE papers spanning 2009 to 2026.

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

These are WBJEE 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 WBJEE Mathematics?

Ellipse has appeared in 17 of the 18 years of WBJEE papers covered here, with 38 questions across 17 papers - about 2 per paper it appears in.

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

Of the 38 questions analysed for this chapter, 32% are easy, 58% moderate and 11% tough. 2020 had the most, with 4 questions.

5.Which topics in Ellipse should I focus on?

These topics have carried the most weightage in Ellipse:

  • Equation of Ellipse - 12 questions (32%)
  • Locus - 9 questions (24%)
  • Tangent to ellipse - 6 questions (16%)
  • Locus has produced the most tough questions (3).
6.Is Ellipse's weightage in WBJEE going up or down?

Across all 17 papers analysed, Ellipse has averaged about 2.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.