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Mathematics - Hyperbola

Practise 40 NTA Abhyas (JEE Main) questions on Hyperbola. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Hyperbola has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 40 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. 1Tangents are drawn from the point , to the hyperbola 3 x 2 - 2 y 2 = 6 and are inclined at angles and to the x -axis. If tan tan = 2 , then
  2. 2Let x 2 + y 2 = 4 r 2 and x y = 1 intersects at A and B in first quadrant. If A B = 14 units, then the value of r is
  3. 3The locus of the mid-points of the chords of the hyperbola 3 x 2 - 2 y 2 + 4 x - 6 y = 0 which are parallel to the line y = 2 x + 4 is
  4. 4The locus of the midpoint of the chords of the hyperbola x 2 25 - y 2 36 = 1 which passes through the point 2 , 4 is a hyperbola, whose tran
  5. 5The sum of the y -intercepts of the tangents drawn from the point - 2 , - 1 to the hyperbola x 2 3 - y 2 2 = 1 is
  6. 6If e 1 and e 2 are the eccentricities of the ellipse x 2 18 + y 2 4 = 1 and the hyperbola x 2 9 - y 2 4 = 1 respectively and e 1 , e 2 is a
  7. 7If the eccentricity of the hyperbola x 2 1 + sin 2 - y 2 cos 2 = 1 is 2 3 , then the sum of all the possible values of is (where, 0 , )
  8. 8If the eccentricity of the hyperbola x 2 - y 2 sec 2 ⁡ α = 5 is 3 times the eccentricity of the ellipse x 2 sec 2 ⁡ α + y 2 = 25 , then tan
  9. 9The area (in sq. units) of the triangle formed by the lines y = 2 x , y = - 2 x and the tangent at the point 5 , 4 on 4 x 2 - y 2 = 4 is equ
  10. 10Let C 1 be the graph of x y = 1 and the reflection of C 1 in the line y = 2 x is C 2 . If the equation of C 2 is expressed as 12 x 2 + b x y
  11. 11The point of intersection of the tangents drawn to the hyperbola x 2 a 2 - y 2 b 2 = 1 at the points where it is intersected by the line l x
  12. 12The locus of a point P α , β moving under the condition that the line y = α x + β is a tangent to the hyperbola x 2 1 - y 2 b 2 = 1 is a con
  13. 13If a circle drawn by assuming a chord parallel to the transverse axis of hyperbola x 2 a 2 - y 2 b 2 = 1 as diameter always passes through 2
  14. 14If the line 2 x + 6 y = 2 touches the hyperbola x 2 - 2 y 2 = a 2 , then a 2 is equal to
  15. 15The area of triangle formed by the lines x - y = 0 , x + y = 0 and any tangent to the hyperbola x 2 - y 2 = 16 is equal to
  16. 16From a point on the line x - y + 2 = 0 tangents are drawn to the hyperbola x 2 6 - y 2 2 = 1 such that the chord of contact passes through a
  17. 17If the eccentricity of the hyperbola x 2 16 - y 2 b 2 = - 1 is 5 4 , then b 2 is equal to
  18. 18From a point P , two tangents P A and P B are drawn to the hyperbola x 2 a 2 - y 2 b 2 = 1 . If the product of the slopes of these tangents
  19. 19Two straight lines having variable slopes m 1 and m 2 pass through the fixed points a , 0 and - a , 0 respectively. If m 1 m 2 = 2 , then th
  20. 20A tangent drawn to the hyperbola x 2 a 2 - y 2 b 2 = 1 at P a sec ⁡ π 6 , b tan ⁡ π 6 form a triangle of area 3 a 2 sq. units with the coord
  21. 21The locus of the point of intersection of two tangents of the hyperbola x 2 2 - y 2 4 = 1 , if the product of their slopes is 1 , is
  22. 22The chords passing through 2,1 intersect the hyperbola x 2 16 - y 2 9 = 1 at A and B . The locus of the point of intersection of tangents at
  23. 23For the hyperbola x 2 a 2 - y 2 b 2 = 1 , distance between the foci is 10 units. From the point 2 , 3 , perpendicular tangents are drawn to
  24. 24The area (in sq. units) of the triangle formed by the latus rectum and the tangents at the end points of the latus rectum of x 2 16 - y 2 9
  25. 25Let the eccentricity of the hyperbola with the principal axes along the coordinate axes and passing through 3,0 and 3 2 , 2 is e , then the
  26. 26The locus of the mid-point of the chords of the hyperbola x 2 - y 2 = 4 , that touches the parabola y 2 = 8 x is
  27. 27A hyperbola has foci 4,2 , 2 , 2 and it passes through P 2 , 4 . The eccentricity of the hyperbola is
  28. 28Values of m , for which the line y = m x + 2 5 is a tangent to the hyperbola 16 x 2 - 9 y 2 = 144 , are the roots of the equation x 2 - a +
  29. 29Let the variable line y = k x + h is tangent to the hyperbola x 2 4 - y 2 9 = 1 . If the locus of P h , k is a conic, then which of the foll
  30. 30If the line y = x + c touches the hyperbola x 2 9 - y 2 5 = 1 at the point P h , k , then h , k can be equal to
  31. 31From a point P , tangents are drawn to the curve x 2 2 - y 2 = 1 . If the chord of contact is a normal chord and the locus of P is the curve
  32. 32A hyperbola having the transverse axis of length 2 units has the same focii as that of ellipse 3 x 2 + 4 y 2 = 12 , then its equation is
  33. 33From a point P , two tangents P A and P B are drawn to the hyperbola x 2 a 2 - y 2 b 2 = 1 . If these tangents cut the coordinate axes at 4
  34. 34The locus of a point which moves such that the difference of its distances from the points 5,0 and - 5,0 is 6 units is a conic, whose length
  35. 35If two points P and Q lie on the hyperbola x 2 a 2 - y 2 b 2 = 1 ( a b ) , whose centre C be such that C P is perpendicular to C Q , then th
  36. 36If the focus of a hyperbola is ( ± 3,0 ) and the equation of a tangent is 2 x + y - 4 = 0 , then the equation of the hyperbola is
  37. 37The locus of the mid-points of the parallel chords with slope m of the rectangular hyperbola x y = c 2 is
  38. 38The equation of a hyperbola is x 2 a 2 - y 2 b 2 = 1 . If P 2 , 5 is a point from which perpendicular tangents can be drawn to the hyperbola
  39. 39The tangent drawn to the hyperbola x 2 16 - y 2 9 = 1 , at point P in the first quadrant whose abscissa is 5, meets the lines 3 x - 4 y = 0
  40. 40Number of points from where perpendicular tangents to the curve x 2 16 - y 2 25 = 1 can be drawn, is/are

Frequently Asked Questions

1.How many questions are available for Hyperbola?

This chapter includes 40 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 Hyperbola 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 Hyperbola questions in NTA Abhyas (JEE Main)?

Of the 40 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Hyperbola should I focus on?

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