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Mathematics - Hyperbola

Practise 29 WBJEE previous year questions on Hyperbola, compiled from papers spanning 2011 to 2024. 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.

Hyperbola has been asked in 14 of the 18 years of WBJEE papers analysed (2009–2026), with 29 questions in all. 41% of them were easy, 45% moderate and 14% tough. Most of its questions came from 2019, with 5 questions that year. In the last three years (2024–2026) it had 1 question across 3 papers, about 0.3 per paper.

The chapter's 7 topics are not weighted equally: Equation of hyperbola (14 questions, 48%), Tangent to hyperbola (5 questions, 17%), and Normal to hyperbola (4 questions, 14%) have been asked the most. Over the last five years the most frequent topics have been Normal to hyperbola (2), Equation of hyperbola (1), and Locus (1). Tangent to hyperbola has produced the most tough questions (2).

  1. 1The locus of the midpoint of the system of parallel chords parallel to the line to the hyperbola is2024Locus
  2. 2If a hyperbola passes through the point \( {P}( {2}, {3})\) and foci at \(( 2,0)\) then the tangent to this hyperbola at \( {P}\) is2023Tangent to hyperbola
  3. 3The average length of all vertical chords of the hyperbola \( {x^2}{a^2}- {y^2}{b^2}=1, a x 2 a\), is2023Chord of hyperbola
  4. 4Let \(A(2 , 3 )\) and \(B(2 , 3 )\) where \( + = { }{2}\) be two points on the hyperbola \( {x^2}{4}- {y^2}{9}=1\). If \(( , )\) is the poin2023Normal to hyperbola
  5. 5Let be two points on such that . Then the ordinate of the point of intersection of the normals at and is2022Normal to hyperbola
  6. 6is a double ordinate of the hyperbola such that is an equilateral triangle, being the centre of the hyperbola. Then the eccentricity e of th2022Equation of hyperbola
  7. 7The locus of the center of a variable circle which always touches two given circles externally is2021Locus
  8. 8The normal to a curve at meets the -axis at . If the distance of from the origin is twice the abscissa of then the curve is2021Equation of hyperbola
  9. 9The locus of the centre of the circles which touch both the circles and ax externally is2020Equation of hyperbola
  10. 10A double ordinate of the hyperbola is such that is equilateral, being the centre of the hyperbola. Then the eccentricity e satisfies the rel2020Equation of hyperbola
  11. 11Let be a point on the hyperbola . If the normal at intersects the -axis at (16,0) , then the eccentricity of the hyperbola is2019Normal to hyperbola
  12. 12For the hyperbola which of the following remains fixed when varies?2019Equation of hyperbola
  13. 13The equation of the directrices of the hyperbola is2019Equation of hyperbola
  14. 14The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is2019Equation of hyperbola
  15. 15Equation of a tangent to the hyperbola and which passes through an external point (2,8) is2019Tangent to hyperbola
  16. 16Let the eccentricity of the hyperbola be reciprocal to that of the ellipse then the ratio equals2018Equation of hyperbola
  17. 17A hyperbola, having the transverse axis of length is confocal with the ellipse . It equation is2018Equation of hyperbola
  18. 18Let be the foot of the perpendicular from focus of hyperbola on the line and let be the centre of the hyperbola. Then, the area of the recta2017Tangent to hyperbola
  19. 19The line segment joining the foci of the hyperbola is one of the diameters of a circle. The equation of the circle is2017Line and hyperbola
  20. 20Let and be two points. point moves in the plane in such a way that Then, the point moves along2017Equation of hyperbola
  21. 21If is a double ordinate of the hyperbola such that is equilateral. being the centre. Then, the eccentricity satisfies2016Tangent to hyperbola
  22. 22Let represents a hyperbola. Then,2015General Equation of 2nd degree curve
  23. 23If the straight line is normal to the hyperbola , then which of the following does not hold?2015Normal to hyperbola
  24. 24The equation of the common tangent with positive slope to the parabola and the hyperbola is2014Tangent to hyperbola
  25. 25The equation of hyperbola whose coordinates of the foci are (±8,0) and the length of latusrectum is 24 units, is2014Equation of hyperbola
  26. 26For the variable the locus of the points of intersection of lines and is2013Locus
  27. 27The transverse axis of a hyperbola is along the -axis and its length is . The vertex of the hyperbola bisects the line segment joining the c2012Equation of hyperbola
  28. 28A point moves in such a way that the difference of its distance from two points (8,0) and (-8,0) always remains Then, the locus of the point2012Equation of hyperbola
  29. 29The eccentricity of the hyperbola \(4 x^2-9 y^2=36\) is2011Equation of hyperbola

Frequently Asked Questions

1.How many questions are available for Hyperbola?

This chapter includes 29 questions compiled from WBJEE papers spanning 2011 to 2024.

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

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

3.Is Hyperbola an important chapter for WBJEE Mathematics?

Hyperbola has appeared in 14 of the 18 years of WBJEE papers covered here, with 29 questions across 14 papers - about 2 per paper it appears in.

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

Of the 29 questions analysed for this chapter, 41% are easy, 45% moderate and 14% tough. 2019 had the most, with 5 questions.

5.Which topics in Hyperbola should I focus on?

These topics have carried the most weightage in Hyperbola:

  • Equation of hyperbola - 14 questions (48%)
  • Tangent to hyperbola - 5 questions (17%)
  • Normal to hyperbola - 4 questions (14%)
  • Tangent to hyperbola has produced the most tough questions (2).
6.Is Hyperbola's weightage in WBJEE going up or down?

Across all 14 papers analysed, Hyperbola has averaged about 2.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.