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Mathematics - Circle

Practise 200 JEE Main previous year questions on Circle, compiled from papers spanning 2002 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 JEE Main tests.

Circle has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 200 questions in all. 13% of them were easy, 56% moderate and 31% tough. Most of its questions came from 2021, with 26 questions that year. In the last three years (2024–2026) it had 38 questions across 49 papers, about 0.8 per paper.

The chapter's 13 topics are not weighted equally: Equation of Circle & its intercept (46 questions, 23%), line and circle (32 questions, 16%), and Locus (22 questions, 11%) have been asked the most. Equation of Circle & its intercept has also led over the last five years, with 29 questions. Equation of Circle & its intercept has produced the most tough questions (14).

  1. 1Consider the circle . Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendic08 Apr, 2026 (E)Locus
  2. 2Let the centre of the circle be in the first quadrant and lie on the line . Let the area of an equilateral triangle inscribed in the circle 06 Apr, 2026 (M)Equation of Circle & its intercept
  3. 3Let be a circle having centre in the first quadrant and touching the -axis at a distance of units from the origin. If the circle has an inte06 Apr, 2026 (E)Equation of Circle & its intercept
  4. 4Let the line intersect the circle at the points and . If is a point on such that , then is equal to __________.06 Apr, 2026 (E)line and circle
  5. 5Let be a moving point on the circle . Then, the maximum distance of from the vertex of the parabola is equal to:05 Apr, 2026 (M)Position of point
  6. 6Suppose that two chords, drawn from the point on the circle are bisected by the -axis. If the other ends of these chords are and , and the m04 Apr, 2026 (M)Equation of Circle & its intercept
  7. 7Let a circle have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from 02 Apr, 2026 (M)Equation of Circle & its intercept
  8. 8Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines and . If the line inter02 Apr, 2026 (E)Equation of Circle & its intercept
  9. 9Let be the equation of a chord of the circle (in the closed half-plane ) of diameter 10 passing through the origin. Let be another circle de28 Jan, 2026 (M)Chord with given Middle Point
  10. 10Let the circle intersect -axis at the points and . Let , and be two points such that . Then the point of intersection of AQ and BP lies on :28 Jan, 2026 (E)Equation of Circle & its intercept
  11. 11Let and . Then is equal to24 Jan, 2026 (M)Equation of Circle & its intercept
  12. 12Let a circle of radius 4 pass through the origin O, the points and , where and are real parameters and . Then the locus of the centroid of i24 Jan, 2026 (M)Locus
  13. 13If the points of intersection of the ellipses and lie on a circle of radius and centre , then the value of is23 Jan, 2026 (E)Family of Circle
  14. 14Let the set of all values of , for which the circles and intersect at two distinct points be the interval . Then is equal to22 Jan, 2026 (M)Intersection of Circles
  15. 15Let and be vectors such that and . If are the possible values of , then the equation represents a circle, for K equal to :21 Jan, 2026 (M)General Equation of 2nd degree curve
  16. 16Let PQ and MN be two straight lines touching the circle at the points A and B respectively. Let O be the centre of the circle and . Then the21 Jan, 2026 (M)Locus
  17. 17If P is a point on the circle is a point on the straight line and is the perpendicular bisector of PQ, then 13 times the sum of abscissa of 21 Jan, 2026 (E)Equation of Circle & its intercept
  18. 18Let be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let be the circle with centre that touches external07 Apr, 2025 (M)Equation of Circle & its intercept
  19. 19If the four distinct points and lie on a circle of radius r , then is equal to03 Apr, 2025 (E)Equation of Circle & its intercept
  20. 20The absolute difference between the squares of the radii of the two circles passing through the point and touching the lines and , is equal 02 Apr, 2025 (M)Equation of Circle & its intercept
  21. 21Let the line \(x+y=1\) meet the circle \(x^2+y^2=4\) at the points A and B . If the line perpendicular to \(A B\) and passing through the mi29 Jan, 2025 (M)line and circle
  22. 22Let a circle pass through the points and , and its centre lie on . Then the length of the chord, of the circle , whose mid-point is , is :29 Jan, 2025 (E)line and circle
  23. 23Let the equation of the circle, which touches -axis at the point and cuts off an intercept of length on -axis be . If the circle lies below 28 Jan, 2025 (M)Equation of Circle & its intercept
  24. 24Let circle be the image of in the line and be the point on such that is parallel to -axis and lies on the right hand side of the centre of .24 Jan, 2025 (M)Equation of Circle & its intercept
  25. 25Let the arc of a circle subtend a right angle at the centre . If the point on the arc , divides the arc such that , and , then is equal to23 Jan, 2025 (M)General Equation of 2nd degree curve
  26. 26A circle of radius 2 lies in the second quadrant and touches both the coordinate axes. Let be the radius of a circle that has centre at the 22 Jan, 2025 (M)Family of Circle
  27. 27Let a circle passing through have its centre at the point . Let be the point of intersection of the lines and . If and , then the equation o09 Apr, 2024 (M)Equation of Circle & its intercept
  28. 28Let the centre of a circle, passing through the points and touching the circle , be . Then for all possible values of the coordinates of the09 Apr, 2024 (M)Common Chord
  29. 29Let the circles and touch each other externally at the point . If the point divides the line segment joining the centres of the circles and 08 Apr, 2024 (M)Common Chord
  30. 30A circle is inscribed in an equilateral triangle of side of length 12 . If the area and perimeter of any square inscribed in this circle are06 Apr, 2024 (M)Equation of Circle & its intercept
  31. 31Let be the circle of minimum area touching the parabola and the lines . Then, which one of the following points lies on the circle ?06 Apr, 2024 (M)Position of point
  32. 32Let a circle of radius 1 and closer to the origin be such that the lines passing through the point and parallel to the coordinate axes touch05 Apr, 2024 (M)Position of point
  33. 33Let and be squares of side 4 and 2 units, respectively. The point is on the line segment and the point is on the diagonal . Then the radius 05 Apr, 2024 (E)line and circle
  34. 34Let the circle and be a circle having centre at and radius 2 . If the line of the common chord of and intersects the -axis at the point , th05 Apr, 2024 (E)Common Chord
  35. 35A square is inscribed in the circle . One side of this square is parallel to . If are the vertices of the square, then is equal to:04 Apr, 2024 (M)Equation of Circle & its intercept
  36. 36Let be a circle with radius units and centre at the origin. Let the line intersects the circle at the points and . Let be a chord of of leng04 Apr, 2024 (E)line and circle
  37. 37Let C : x 2 + y 2 = 4 and C ' : x 2 + y 2 − 4 λ x + 9 = 0 be two circles. If the set of all values of λ so that the circles C and C ' inters01 Feb, 2024 (M)Common Tangents
  38. 38Let the line L : 2 x + y = α pass through the point of the intersection P (in the first quadrant)of the circle x 2 + y 2 = 3 and the parabol01 Feb, 2024 (M)Common Tangents
  39. 39Let the locus of the mid points of the chords of circle x 2 + y − 1 2 = 1 drawn from the origin intersect the line x + y = 1 at P and Q . Th01 Feb, 2024 (E)Chord with given Middle Point
  40. 40If one of the diameters of the circle x 2 + y 2 - 10 x + 4 y + 13 = 0 is a chord of another circle C , whose center is the point of intersec31 Jan, 2024 (M)line and circle
  41. 41Let a variable line passing through the centre of the circle x 2 + y 2 − 16 x − 4 y = 0 , meet the positive co-ordinate axes at the point A 31 Jan, 2024 (E)Equation of Circle & its intercept
  42. 42If the circles ( x + 1 ) 2 + ( y + 2 ) 2 = r 2 and x 2 + y 2 - 4 x - 4 y + 4 = 0 intersect at exactly two distinct points, then30 Jan, 2024 (M)Equation of Circle & its intercept
  43. 43Consider two circles C 1 : x 2 + y 2 = 25 and C 2 : ( x - α ) 2 + y 2 = 16 , where α ∈ ( 5 , 9 ) . Let the angle between the two radii (one 30 Jan, 2024 (E)Common Chord
  44. 44Equations of two diameters of a circle are 2 x - 3 y = 5 and 3 x - 4 y = 7 . The line joining the points - 22 7 , - 4 and - 1 7 , 3 intersec29 Jan, 2024 (M)line and circle
  45. 45Four distinct points ( 2 k , 3 k ) , ( 1 , 0 ) , ( 0 , 1 ) and ( 0 , 0 ) lie on a circle for k equal to :27 Jan, 2024 (M)Equation of Circle & its intercept
  46. 46Consider a circle x - α 2 + y - β 2 = 50 , where α , β 0 . If the circle touches the line y + x = 0 at the point P , whose distance from the27 Jan, 2024 (E)line and circle
  47. 47The number of common tangents, to the circles x 2 + y 2 - 18 x - 15 y + 131 = 0 and x 2 + y 2 - 6 x - 6 y - 7 = 0 , is15 Apr, 2023 (M)Common Tangents
  48. 48Let the centre of a circle C be , and its radius r 8 . Let 3 x + 4 y = 24 and 3 x 4 y = 32 be two tangents and 4 x + 3 y = 1 be a normal to 13 Apr, 2023 (E)Tangent to circle
  49. 49Two circles in the first quadrant of radii r 1 and r 2 touch the coordinate axes. Each of them cuts off an intercept of 2 units with the lin12 Apr, 2023 (M)line and circle
  50. 50Consider ellipses E k : k x 2 + k 2 y 2 = 1 , k = 1 , 2 , , 20 . Let C k be the circle which touches the four chords joining the end points 11 Apr, 2023 (M)Tangent to circle

Frequently Asked Questions

1.How many questions are available for Circle?

This chapter includes 200 questions compiled from JEE Main papers spanning 2002 to 2026.

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

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

3.Is Circle an important chapter for JEE Main Mathematics?

Circle has appeared in 25 of the 25 years of JEE Main papers covered here, with 200 questions across 157 papers - about one per paper it appears in.

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

Of the 200 questions analysed for this chapter, 13% are easy, 56% moderate and 31% tough. 2021 had the most, with 26 questions.

5.Which topics in Circle should I focus on?

These topics have carried the most weightage in Circle:

  • Equation of Circle & its intercept - 46 questions (23%)
  • line and circle - 32 questions (16%)
  • Locus - 22 questions (11%)
  • Equation of Circle & its intercept has produced the most tough questions (14).
6.Is Circle's weightage in JEE Main going up or down?

Across all 157 papers analysed, Circle has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.