Jump to a section

Mathematics - Circle

Practise 39 WBJEE previous year questions on Circle, 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.

Circle has been asked in 16 of the 18 years of WBJEE papers analysed (2009–2026), with 39 questions in all. 21% of them were easy, 54% moderate and 26% tough. Most of its questions came from 2013, with 6 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 13 topics are not weighted equally: Equation of Circle & its intercept (8 questions, 21%), Locus (7 questions, 18%), and Intersection of Circles (3 questions, 8%) have been asked the most. Equation of Circle & its intercept has also led over the last five years, with 3 questions. Locus has produced the most tough questions (3).

  1. 1Let all the points on the curve are reflected about the line . If the locus of the reflected points is in the form , then the value of is2026Equation of Circle & its intercept
  2. 2The number of common tangents to the circles is2025Common Tangents
  3. 3Let and be two perpendicular diameters of a circle of radius . The circle will pass through the origin if is equal to2025Equation of Circle & its intercept
  4. 4Chords AB & CD of a circle intersect at right angle at the point P. If the length of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then 2024line and circle
  5. 5If two circles which pass through the points (0, a) and (0, - a) and touch the line y = mx + c, cut orthogonally then2024Intersection of Circles
  6. 6Two circle and have a common chord . The equation of is2022Common Chord
  7. 7If the equation of one tangent to the circle with centre at from the origin is , then the equation of the other tangent through the origin i2022Pair of Tangents
  8. 8A straight line meets the co-ordinate axes at and . A circle is circumscribed about the triangle being the origin. If and are the distances 2022Equation of Circle & its intercept
  9. 9Let be a variable point on a circle and be a fixed point outside . If is the midpoint of the line segment , then locus of is2021Locus
  10. 10The equation of circle of radius unit, with centre on the positive side of -axis and through the point is2020Equation of Circle & its intercept
  11. 11A variable circle passes through the fixed point and touches -axis. The locus of the other end of the diameter through is2019Equation of Circle & its intercept
  12. 12The angle between a pair of tangents drawn from a point to the circle is The equation of the locus of the point is2018Pair of Tangents
  13. 13If one of the diameter of the circle, given by the equation is a chord of a circle whose centre is ), the radius of is2018Chord with given Middle Point
  14. 14A chord is drawn from the point on the circle and is extended to such that . The locus of is2018Locus
  15. 15Let be the centre of the circle Let and be two points on the circle such that tangents at and meet at . The area of the quadrilateral is2018Pair of Tangents
  16. 16The common chord of the circles and subtends at the origin an angle equal to2017Common Chord
  17. 17The locus of the mid-points of the chords of the circle which make an angle of at the centre is2017Locus
  18. 18If one of the diameters of the curve is a chord of a circle with centre the radius of this circle is2017Chord with given Middle Point
  19. 19The equation of a line parallel to the line and touching the circle in the first quadrant, is2016Tangent to circle
  20. 20The locus of the mid-points of chords of the circle , which subtends a right angle at the origin, is2016Locus
  21. 21The angle of intersection between the curves and where denotes the greatest integer is2014Line and Circle
  22. 22If the circle cuts the three circles and at the extremities of their diameters, then2014General Equation of 2nd degree curve
  23. 23A point lies on the circle . If and then the is2013Position of point
  24. 24A point moves, so that the sum of squares of its distance from the points (1,2) and (-2,1) is always Then, its locus is2013Locus
  25. 25A circle passing through (0,0),(2,6) (6,2) cut the -axis at the point Then, the lenght of where is the origin, is2013Locus
  26. 26If one end of a diameter of the circle is then the other end is2013General Equation of 2nd degree curve
  27. 27The equation of the circle passing through the point (1,1) and the points of intersection of and is2013Family of Circle
  28. 28The equations of the circles, which touch both the axes and the line and have centres in the first quadrant, are2013General Equation of 2nd degree curve
  29. 29If the circles and intersect orthogonally. then is equal to2012Intersection of Circles
  30. 30If four distinct points (0,0) lie on a circle, then2012Equation of Circle & its intercept
  31. 31Let and denote the centres of the circles and respectively and let and be their points of intersection.Then, the areas of and are in the rat2012Family of Circle
  32. 32If the straight line \(y=m x\) lies outside of the circle \(x^2+y^2-20 y+90=0\), then the value of \(m\) will satisfy2011Line and Circle
  33. 33The locus of the centre of a circle which passes through two variable points \((a, 0),(-a, 0)\) is2011Locus
  34. 34The intercept on the line \(y=x\) by the circle \(x^2+y^2-2 x=0\) is \(A B\). Equation of the circle with \(A B\) as diameter is2011Equation of Circle & its intercept
  35. 35If the coordinates of one end of a diameter of the circle \(x^2+y^2+4 x-8 y+5=0\), is \((2,1)\), the coordinates of the other end is2011Equation of Circle & its intercept
  36. 36The straight line meets the circle at and . Then the equation of the circle of which is a diameter is2010Family of Circle
  37. 37The circles and intersect at two distinct points if2009Intersection of Circles
  38. 38For the two circles and there is / are2009Common Tangents
  39. 39The equation of the chord of the circle whose mid point is is2009Chord with given Middle Point

Frequently Asked Questions

1.How many questions are available for Circle?

This chapter includes 39 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 Circle chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Circle an important chapter for WBJEE Mathematics?

Circle has appeared in 16 of the 18 years of WBJEE papers covered here, with 39 questions across 16 papers - about 2 per paper it appears in.

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

Of the 39 questions analysed for this chapter, 21% are easy, 54% moderate and 26% tough. 2013 had the most, with 6 questions.

5.Which topics in Circle should I focus on?

These topics have carried the most weightage in Circle:

  • Equation of Circle & its intercept - 8 questions (21%)
  • Locus - 7 questions (18%)
  • Intersection of Circles - 3 questions (8%)
  • Locus has produced the most tough questions (3).
6.Is Circle's weightage in WBJEE going up or down?

Across all 16 papers analysed, Circle has averaged about 2.4 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.