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Mathematics - Parabola

Practise 44 WBJEE previous year questions on Parabola, 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.

Parabola has been asked in 17 of the 18 years of WBJEE papers analysed (2009–2026), with 44 questions in all. 27% of them were easy, 57% moderate and 16% tough. Most of its questions came from 2022, with 7 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 12 topics are not weighted equally: Tangent to Parabola (9 questions, 20%), Chord of parabola (8 questions, 18%), and Locus (7 questions, 16%) have been asked the most. Tangent to Parabola has also led over the last five years, with 3 questions. General Equation of 2nd degree curve has produced the most tough questions (2).

  1. 1If the locus of mid point of any normal chord of the parabola is , where , then equals to2026Normal to Parabola
  2. 2The parabola has vertex . It intersects x-axis at and . If the parabola is translated from its initial position to a new position by moving 2026standard equation of parabola
  3. 3The line cuts the parabola at the points and . If the co-ordinates of the point are , then the value of is2025Line and parabola
  4. 4The maximum number of common normals of and is equal to2025Normal to Parabola
  5. 5is an equilateral triangle inscribed in the parabola with as the vertex, then the length of the side of is2024Tangent to Parabola
  6. 6Let \(O\) be the vertex, \(Q\) be any point on the parabola \(x^2=8 y\). If the point \(P\) divides the line segment \(O Q\) internally in t2023Locus
  7. 7From the focus of the parabola \(y^2=12 x\), a ray of light is directed in a direction making an angle \( ^{-1} {3}{4}\) with \(x\)-axis. Th2023Line and parabola
  8. 8is a chord of a parabola with vertex is drawn perpendicular to meeting the axis at . The projection of on the axis of the parabola is2022Chord of parabola
  9. 9Let be the point and be a variable point on . Then the locus of mid-point of is2022Locus
  10. 10The point of contact of the tangent to the parabola which passes through the point and makes an angle with the positive side of the axis of 2022Tangent to Parabola
  11. 11Let the tangent and normal at any point , 2at), , on the parabola meet the axis of the parabola at and respectively. Then the radius of the 2022Tangent to Parabola
  12. 12From the point , two tangents are drawn to . Then the angle between the two tangents is2022Pair of Tangents
  13. 13If and are two focal chords of the parabola then the chords and intersect on the2022Chord of parabola
  14. 14The line touches2022Line and parabola
  15. 15From a point three normals are drawn to the parabola then2021Normal to Parabola
  16. 16The locus of the vertices of the family of parabolas is2021Locus
  17. 17The length of the chord of the parabola which passes through the vertex and makes an acute angle with the axis of the parabola is2020Chord of parabola
  18. 18The equation of the latus rectum of a parabola is and the equation of the tangent at the vertex is . Then the length of the latus rectum is2020Line and parabola
  19. 19If the line is a tangent to the parabola at the point and the curve passes through , then2020Tangent to Parabola
  20. 20Number of common tangents of and is2018Common Tangent
  21. 21Let be two distinct points on the parabola . If the axis of the parabola touches a circle of radius having as diameter, the slope of the lin2018Line and parabola
  22. 22Let R(ar be three points on a parabola . If is the focal chord and are parallel where the co-ordinates of is then the value of is2018Chord of parabola
  23. 23Consider the parabola . Let and be points on the parabola where and . Let be a point on the arc of the parabola between and . Then, the area2018Chord of parabola
  24. 24The axis of the parabola is2017General Equation of 2nd degree curve
  25. 25If the tangent to at the point where is a normal to at the point then2017Tangent to Parabola
  26. 26The focus of the conic is2017General Equation of 2nd degree curve
  27. 27A line passing through the point of intersection of and makes an angle with the -axis. It intersects the parabola at points and respectively2016Chord of parabola
  28. 28The locus of the mid-points of all chords of the parabola through its vertex is another parabola with directrix2016Locus
  29. 29If the parabola makes an intercept of length units on the line , then is equal to2016Line and parabola
  30. 30If the vertex of the conic always lies between the straight lines and then2015Tangent to Parabola
  31. 31If is parallel to a tangent to the parabola , then its distance from the normal parallel to the given line is2014Tangent to Parabola
  32. 32The value of for which the curve representa a parabola is2014Locus
  33. 33The point on the parabola which is nearest to the line has coordinates2014Tangent to Parabola
  34. 34Suppose that the equation has two distinct real roots and . The angle between the tangent to the curve at the point and the positive directi2014Tangent to Parabola
  35. 35If be a point on the parabola with focus . Let denote the foot of the perpendicular from onto the directrix. Then, is2013Position of point
  36. 36The equation represents a parabola whose latusrectum is2012Standard equation of parabola
  37. 37Let be the mid-point of a chord joining the vertex of the parabola to another point on it. Then, the locus of is2012Chord of parabola
  38. 38Let and be the points on the parabola so that the line segment subtends right angle at the vertex. If intersects the axis of the parabola at2012Chord with given Middle Point
  39. 39The vertex of the parabola \(y^2+6 x-2 y+13=0\) is \( {aligned} & (y-1)^2=-6 x-12 \\ & (y-1)^2=-6(x+2)=4 ( {-6}{4} )(x+2) \\ & { Vertex } (-2011Standard equation of parabola
  40. 40The coordinates of a moving point \(p\) are \( (2 t^2+4,4 t+6 )\). Then its locus will be a2011Standard equation of parabola
  41. 41For the real parameter \(t\), the locus of the complex number \( {z}= (1- {t}^2 )+i {1+ {t}^2}\) in the complex plane is2011Locus
  42. 42The locus of the middle points of all chords of the parabola \(y^2=4\) ax passing through the vertex is2011Locus
  43. 43If and be the parameters of the end points of a focal chord for the parabola , then which one is true?2010Chord of parabola
  44. 44The co-ordinates of the focus of the parabola described parametrically by are2009Standard equation of parabola

Frequently Asked Questions

1.How many questions are available for Parabola?

This chapter includes 44 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 Parabola chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Parabola an important chapter for WBJEE Mathematics?

Parabola has appeared in 17 of the 18 years of WBJEE papers covered here, with 44 questions across 17 papers - about 3 per paper it appears in.

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

Of the 44 questions analysed for this chapter, 27% are easy, 57% moderate and 16% tough. 2022 had the most, with 7 questions.

5.Which topics in Parabola should I focus on?

These topics have carried the most weightage in Parabola:

  • Tangent to Parabola - 9 questions (20%)
  • Chord of parabola - 8 questions (18%)
  • Locus - 7 questions (16%)
  • General Equation of 2nd degree curve has produced the most tough questions (2).
6.Is Parabola's weightage in WBJEE going up or down?

Across all 17 papers analysed, Parabola has averaged about 2.6 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.