Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE PYQs · Mathematics · Circle

JEE Circle PYQs with Solutions

506 previous year questions from Circle (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

506 questionsMathematics2004–2026Answers + solutions

About Circle PYQs

Circle has 506 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (191) and JEE Advanced (29), spanning 2004 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 18
  • 2025: 9
  • 2024: 21
  • 2023: 21
  • 2022: 25
  • 2021: 26
  • 2020: 7
  • 2019: 24
  • 2018: 7
  • 2017: 6
  • 2016: 6
  • 2015: 5

Circle questions with solutions

1

Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The circle with centre (1, 2) and touching the straight line 3x + 4y =

JEE Advanced 2026 Solution View → 2

Consider the circle C: x^2+y^2-6x-8y-11=0 . Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from

JEE Main 2026 Solution View → 3

Let C be a circle having centre in the first quadrant and touching the x -axis at a distance of 3 units from the origin. If the circle C has an intercept of length 6 3 on y -axis

JEE Main 2026 Solution View → 4

Let the line x - y = 4 intersect the circle C: (x-4)^2 + (y+3)^2 = 9 at the points Q and R . If P(α, β) is a point on C such that PQ = PR , then (6α + 8β)^2 is equal to __________.

JEE Main 2026 Solution View → 5

Let the centre of the circle x^2 + y^2 + 2gx + 2fy + 25 = 0 be in the first quadrant and lie on the line 2x - y = 4 . Let the area of an equilateral triangle inscribed in the

JEE Main 2026 Solution View → 6

Let P be a moving point on the circle x^2 + y^2 - 6x - 8y + 21 = 0 . Then, the maximum distance of P from the vertex of the parabola x^2 + 6x + y + 13 = 0 is equal to:

JEE Main 2026 Solution View → 7

Suppose that two chords, drawn from the point (1, 2) on the circle x^2 + y^2 + x - 3y = 0 are bisected by the y -axis. If the other ends of these chords are R and S , and the mid

JEE Main 2026 Solution View → 8

Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k-1)y + 3 = 0 and 2x + k^2 y - 4 = 0 . If the line x - y

JEE Main 2026 Solution View → 9

Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of

JEE Main 2026 Solution View → 10

Let the circle x^ 2 +y^ 2 =4 intersect x -axis at the points A(a, 0), a>0 and B(b, 0) . Let P(2 α, 2 α) , 0<α<(π)/(2) and Q(2 β, 2 β) be two points such that (α-β)=(π)/(2) . Then

JEE Main 2026 Solution View → 11

Let y=x be the equation of a chord of the circle C_ 1 (in the closed half-plane x ≥ 0 ) of diameter 10 passing through the origin. Let C_ 2 be another circle described on the

JEE Main 2026 Solution View → 12

Let S=\ z ∈ ℂ:|(z-6 i)/(z-2 i)|=1. and .|(z-8+2 i)/(z+2 i)|=(3)/(5)\ . Then ∑_ z ∈ ~s |z|^ 2 is equal to

JEE Main 2026 Solution View → 13

Let a circle of radius 4 pass through the origin O, the points A(- 3 a, 0) and B(0,- 2 b) , where a and b are real parameters and a b ≠ 0 . Then the locus of the centroid of O A B

JEE Main 2026 Solution View → 14

If the points of intersection of the ellipses x^ 2 +2 y^ 2 -6 x-12 y+23=0 and 4 x^ 2 +2 y^ 2 -20 x-12 y+35=0 lie on a circle of radius r and centre (a, b) , then the value of a

JEE Main 2026 Solution View → 15

Let the set of all values of r , for which the circles (x+1)^ 2 +(y+4)^ 2 =r^ 2 and x^ 2 +y^ 2 -4 x-2 y-4=0 intersect at two distinct points be the interval (α, β) . Then α β is

JEE Main 2026 Solution View → 16

If P is a point on the circle x^ 2 +y^ 2 =4, Q is a point on the straight line 5 x+y+2=0 and x-y+1=0 is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all

JEE Main 2026 Solution View → 17

Let c and d be vectors such that | c + d |= 29 and c ×(2 i +3 j +4 k )=(2 i +3 j +4 k ) × d . If λ_ 1 , λ_ 2 (λ_ 1 >λ_ 2 ) are the possible values of ( c + d ) ·(-7 i +2 j +3 k )

JEE Main 2026 Solution View → 18

Let PQ and MN be two straight lines touching the circle x^ 2 +y^ 2 -4 x-6 y-3=0 at the points A and B respectively. Let O be the centre of the circle and ∠ AOB=π / 3 . Then the

JEE Main 2026 Solution View → 19

Let C_1 be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let C_2 be the circle with centre (1,3) that touches C_1 externally at the point (α

JEE Main 2025 Solution View → 20

If the four distinct points (4,6),(-1,5),(0,0) and (k, 3 k) lie on a circle of radius r , then 10 k+r^2 is equal to

JEE Main 2025 Solution View → 21

The absolute difference between the squares of the radii of the two circles passing through the point (-9,4) and touching the lines x+y=3 and x-y=3 , is equal to ______.

JEE Main 2025 Solution View → 22

Let a circle C pass through the points (4,2) and (0,2) , and its centre lie on 3 x+2 y+2=0 . Then the length of the chord, of the circle C , whose mid-point is (1,2) , is :

JEE Main 2025 Solution View → 23

Let 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 mid point of the chord \(A B\) intersects

JEE Main 2025 Solution View → 24

Let the equation of the circle, which touches x -axis at the point (a, 0), a 0 and cuts off an intercept of length b on y -axis be x^2+y^2-α x+β y+γ=0 . If the circle lies below x

JEE Main 2025 Solution View → 25

Let circle C be the image of x^2+y^2-2 x+4 y-4=0 in the line 2 x-3 y+5=0 and A be the point on C such that O A is parallel to x -axis and A lies on the right hand side of the

JEE Main 2025 Solution View → 26

Let the arc A C of a circle subtend a right angle at the centre O . If the point B on the arc A C , divides the arc A C such that length of arc A B length of arc B C =(1)/(5)

JEE Main 2025 Solution View → 27

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2,5) and intersects the

JEE Main 2025 Solution View → 28

Let the straight line y=2 x touch a circle with center (0, α), α>0 , and radius r at a point A_1 . Let B_1 be the point on the circle such that the line segment A_1 B_1 is a

JEE Advanced 2024 Solution View → 29

Let a circle passing through (2,0) have its centre at the point (h, k) . Let (x_c, y_c) be the point of intersection of the lines 3 x+5 y=1 and (2+c) x+5 c^2 y=1 . If h= _ c arrow

JEE Main 2024 Solution View → 30

Let the centre of a circle, passing through the points (0,0),(1,0) and touching the circle x^2+y^2=9 , be (h, k) . Then for all possible values of the coordinates of the centre

JEE Main 2024 Solution View → 31

Let the circles C_1:(x-α)^2+(y-β)^2=r_1^2 and C_2:(x-8)^2+(y-(15)/(2))^2=r_2^2 touch each other externally at the point (6,6) . If the point (6,6) divides the line segment joining

JEE Main 2024 Solution View → 32

A circle is inscribed in an equilateral triangle of side of length 12 . If the area and perimeter of any square inscribed in this circle are m and n , respectively, then m+n^2 is

JEE Main 2024 Solution View → 33

Let C be the circle of minimum area touching the parabola y=6-x^2 and the lines y= 3 |x| . Then, which one of the following points lies on the circle C ?

JEE Main 2024 Solution View → 34

Let A B C D and A E F G be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC . Then the radius r of the

JEE Main 2024 Solution View → 35

Let the circle C_1: x^2+y^2-2(x+y)+1=0 and C_2 be a circle having centre at (-1,0) and radius 2 . If the line of the common chord of C_1 and C_2 intersects the y -axis at the

JEE Main 2024 Solution View → 36

Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3,2) and parallel to the coordinate axes touch it. Then the shortest distance

JEE Main 2024 Solution View → 37

Let C be a circle with radius 10 units and centre at the origin. Let the line x+y=2 intersects the circle C at the points P and Q . Let MN be a chord of C of length 2 unit and

JEE Main 2024 Solution View → 38

A square is inscribed in the circle x^2+y^2-10 x-6 y+30=0 . One side of this square is parallel to y=x+3 . If (x_i, y_i) are the vertices of the square, then Σ(x_i^2+y_i^2) is

JEE Main 2024 Solution View → 39

Let 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 . Then, the length of PQ is:

JEE Main 2024 Solution View → 40

Let C: x ^ 2 + y ^ 2 = 4 and C ^ ' : x ^ 2 + y ^ 2 - 4 + 9 = 0 be two circles. If the set of all values of λ so that the circles C and C ' intersect at two distinct points, is R

JEE Main 2024 Solution View → 41

Let 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 parabola x ^ 2 = 2y . Let the line L touch

JEE Main 2024 Solution View → 42

Let a variable line passing through the centre of the circle x ^ 2 + y ^ 2 - 16x - 4y = 0 , meet the positive co-ordinate axes at the point AandB . Then the minimum value of OA +

JEE Main 2024 Solution View → 43

If one of the diameters of the circle x ^ 2 + y ^ 2 - 10x + 4y + 13 = 0 is a chord of another circle C , whose center is the point of intersection of the lines 2x + 3y = 12 and 3x

JEE Main 2024 Solution View → 44

Consider 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 to each circle) drawn from

JEE Main 2024 Solution View → 45

If the circles ( x + 1 ) ^ 2 + ( y + 2 ) ^ 2 = r ^ 2 and x ^ 2 + y ^ 2 - 4x - 4y + 4 = 0 intersect at exactly two distinct points, then

JEE Main 2024 Solution View → 46

Equations of two diameters of a circle are 2x - 3y = 5 and 3x - 4y = 7 . The line joining the points (- (22)/(7), - 4) and (- (1)/(7), 3) intersects the circle at only one point P

JEE Main 2024 Solution View → 47

Consider 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 the origin is 4 2 , then ( α +

JEE Main 2024 Solution View → 48

Four distinct points ( 2k, 3k ) , ( 1, 0 ) , ( 0, 1 ) and ( 0, 0 ) lie on a circle for k equal to :

JEE Main 2024 Solution View → 49

Let C _ 1 be the circle of radius 1 with center at the origin. Let C _ 2 be the circle of radius r with center at the point A = ( 4, 1 ) , where 1

JEE Advanced 2023 Solution View → 50

The number of common tangents, to the circles x ^ 2 + y ^ 2 - 18x - 15y + 131 = 0 and x ^ 2 + y ^ 2 - 6x - 6y - 7 = 0 , is

JEE Main 2023 Solution View → 51

Let the centre of a circle C be α, β and its radius r < 8 . Let 3x + 4y = 24 and 3x – 4y = 32 be two tangents and 4x + 3y = 1 be a normal to C . Then ( α - β + r ) is equal to

JEE Main 2023 Solution View → 52

Two 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 line x + y = 2 . Then r _ 1 ^ 2 + r _

JEE Main 2023 Solution View → 53

Consider 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 (one on minor axis and another

JEE Main 2023 Solution View → 54

Let Abe the point (1, 2) and B be any point on the curve x ^ 2 + y ^ 2 = 16 . If the centre of the locus of the point P , which divides the line segment AB in the ratio 3: 2 is

JEE Main 2023 Solution View → 55

A line segment AB of length λ moves such that the points A and B remain on the periphery of a circle of radius λ . Then the locus of the point, that divides the line segment AB in

JEE Main 2023 Solution View → 56

Let O be the origin and OP and OQ be the tangents to the circle x ^ 2 + y ^ 2 - 6x + 4y + 8 = 0 at the points P and Q on it. If the circumcircle of the triangle OPQ passes through

JEE Main 2023 Solution View → 57

Consider a circle C _ 1 : x ^ 2 + y ^ 2 – 4x – 2y = α – 5 . Let its mirror image in the line y = 2x + 1 be another circle C _ 2 : 5 x ^ 2 + 5 y ^ 2 – 10fx – 10gy + 36 = 0 . Let r

JEE Main 2023 Solution View → 58

If the tangents at the points P and Q on the circle x ^ 2 + y ^ 2 - 2x + y = 5 meet at the point R((9)/(4), 2), then the area of the triangle PQR is

JEE Main 2023 Solution View → 59

A circle passing through the point P(α, β) in the first quadrant touches the two coordinate axes at the points A and B . The point P is above the line AB . The point Q on the line

JEE Main 2023 Solution View → 60

Let the point (p, p + 1) lie inside the region E = \ (x, y): 3 - x ≤ y ≤ 9 - x ^ 2 , 0 ≤ x ≤ 3\ . If the set of all values of p is the interval (a, b), then b ^ 2 + b - a ^ 2 is

JEE Main 2023 Solution View → 61

The set of all values of a ^ 2 for which the line x + y = 0 bisects two distinct chords drawn from a point P((1 + a)/(2), (1 - a)/(2)) on the circle 2 x ^ 2 + 2 y ^ 2 - ( 1 + a )

JEE Main 2023 Solution View → 62

Let a circle C _ 1 be obtained on rolling the circle x ^ 2 + y ^ 2 - 4x - 6y + 11 = 0 upwards 4 units on the tangent T to it at the point (3, 2) . Let C _ 2 be the image of C _ 1

JEE Main 2023 Solution View → 63

Let P( a _ 1 , b _ 1 ) and Q( a _ 2 , b _ 2 ) be two distinct points on a circle with center C ( 2 , 3 ) . Let O be the origin and OC be perpendicular to both CP and CQ . If the

JEE Main 2023 Solution View → 64

Let y = x + 2, 4y = 3x + 6 and 3y = 4x + 1 be three tangent lines to the circle ( x - h ) ^ 2 + ( y - k ) ^ 2 = r ^ 2 . Then h + k is equal to :

JEE Main 2023 Solution View → 65

A circle with centre ( 2, 3 ) and radius 4 intersects the line x + y = 3 at the points P and Q . If the tangents at P and Q intersect at the point S ( α, β ) , then 4α - 7β is

JEE Main 2023 Solution View → 66

Let the tangents at the points A ( 4, - 11 ) and B ( 8, - 5 ) on the circle x ^ 2 + y ^ 2 - 3x + 10y - 15 = 0 , intersect at the point C . Then the radius of the circle, whose

JEE Main 2023 Solution View → 67

Points P(- 3, 2), Q(9, 10) and R(α, 4) lie on a circle C with PR as its diameter. The tangents to C at the points Q and R intersect at the point S . If S lies on the line 2x - ky

JEE Main 2023 Solution View → 68

The points of intersection of the line ax + by = 0 , ( a ≠ b ) and the circle x ^ 2 + y ^ 2 - 2x = 0 are A ( α, 0 ) and B ( 1, β ) . The image of the circle with AB as a diameter

JEE Main 2023 Solution View → 69

The locus of the middle points of the chords of the circle C _ 1 : (x - 4) ^ 2 + (y - 5) ^ 2 = 4 which subtend an angle θ _ i at the centre of the circle C _ i , is a circle of

JEE Main 2023 Solution View → 70

Let G be a circle of radius R > 0 . Let G _ 1 , G _ 2 , … , G _ n be n circles of equal radius r > 0 . Suppose each of the n circles G _ 1 , G _ 2 , … , G _ n touches the circle G

JEE Advanced 2022 Solution View → 71

Let AB be a chord of length 12 of the circle (x - 2) ^ 2 + (y + 1) ^ 2 = (169)/(4) If tangents drawn to the circle at points A and B intersect at the point P , then five times the

JEE Main 2022 Solution View → 72

Let a line L pass through the point of intersection of the lines bx + 10y - 8 = 0 and 2x - 3y = 0 , b ∈ R - \ (4)/(3)\ . If the line L also passes through the point (1, 1) and

JEE Main 2022 Solution View → 73

Let the mirror image of a circle c _ 1 : x ^ 2 + y ^ 2 - 2x - 6y + α = 0 in line y = x + 1 be c _ 2 : 5 x ^ 2 + 5 y ^ 2 + 10gx + 10fy + 38 = 0 . If r is the radius of circle c _ 2

JEE Main 2022 Solution View → 74

Let the tangents at two points A and B on the circle x ^ 2 + y ^ 2 - 4x + 3 = 0 meet at origin O(0, 0) . Then the area of the triangle of OAB is

JEE Main 2022 Solution View → 75

Let C be the centre of the circle x ^ 2 + y ^ 2 - x + 2y = (11)/(4) and P be a point on the circle. A line passes through the point C , makes an angle of (π)/(4) with the line CP

JEE Main 2022 Solution View → 76

A circle C _ 1 passes through the origin O and has diameter 4 on the positive x -axis. The line y = 2x gives a chord OA of a circle C _ 1 . Let C _ 2 be the circle with OA as a

JEE Main 2022 Solution View → 77

If the circle x ^ 2 + y ^ 2 - 2gx + 6y - 19c = 0, g, c ∈ ℝ passes through the point (6, 1) and its centre lies on the line x - 2cy = 8 , then the length of intercept made by the

JEE Main 2022 Solution View → 78

Let the abscissae of the two points P and Q on a circle be the roots of x ^ 2 - 4x - 6 = 0 and the ordinates of P and Q be the roots of y ^ 2 + 2y - 7 = 0 . If PQ is a diameter of

JEE Main 2022 Solution View → 79

A point P moves so that the sum of squares of its distances from the points (1, 2) and (- 2, 1) is 14 . Let f (x, y) = 0 be the locus of P , which intersects the x -axis at the

JEE Main 2022 Solution View → 80

If the circles x ^ 2 + y ^ 2 + 6x + 8y + 16 = 0 and x ^ 2 + y ^ 2 + 2(3 - 3 )x + 2(4 - 6 )y = k + 6 3 + 8 6 , k > 0 , touch internally at the point P(α, β) , then (α + 3 ) ^ 2 +

JEE Main 2022 Solution View → 81

Let the locus of the centre (α, β), β > 0 , of the circle which touches the circle x ^ 2 + (y - 1) ^ 2 = 1 externally and also touches the x -axis be L . Then the area bounded by

JEE Main 2022 Solution View → 82

Let a triangle ABC be inscribed in the circle x ^ 2 - 2 (x + y) + y ^ 2 = 0 such that ∠ BAC = (π)/(2) . If the length of side AB is 2 , then the area of the △ ABC is equal to:

JEE Main 2022 Solution View → 83

Let the tangent to the circle C _ 1 : x ^ 2 + y ^ 2 = 2 at the point M(- 1, 1) intersect the circle C _ 2 : (x - 3) ^ 2 + (y - 2) ^ 2 = 5 , at two distinct points A and B . If the

JEE Main 2022 Solution View → 84

If one of the diameters of the circle x ^ 2 + y ^ 2 - 2 2 x - 6 2 y + 14 = 0 is a chord of the circle (x - 2 2 ) ^ 2 + (y - 2 2 ) ^ 2 = r ^ 2 , then the value of r ^ 2 is equal to

JEE Main 2022 Solution View → 85

If the tangents drawn at the point O(0, 0) and P(1 + 5 , 2) on the circle x ^ 2 + y ^ 2 - 2x - 4y = 0 intersect at the point Q , then the area of the triangle OPQ is equal to

JEE Main 2022 Solution View → 86

Let the lines y + 2x = 11 + 7 7 and 2y + x = 2 11 + 6 7 be normal to a circle C: (x - h) ^ 2 + (y - k) ^ 2 = r ^ 2 . If the line 11 y - 3x = 5 77 3 + 11 is tangent to the circle C

JEE Main 2022 Solution View → 87

The set of values of k for which the circle C: 4 x ^ 2 + 4 y ^ 2 - 12x + 8y + k = 0 lies inside the fourth quadrant and the point (1, - (1)/(3)) lies on or inside the circle C is

JEE Main 2022 Solution View → 88

Let a circle C of radius 5 lie below the x -axis. The line L _ 1 = 4x + 3y + 2 passes through the centre P of the circle C and intersects the line L _ 2 : 3x - 4y - 11 = 0 at Q .

JEE Main 2022 Solution View → 89

A rectangle R with end points of the one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x - y + 4 = 0 , then the area

JEE Main 2022 Solution View → 90

Let C be a circle passing through the points A(2, - 1) and B(3, 4) . The line segment AB is not a diameter of C . If r is the radius of C and its centre lies on the circle (x - 5)

JEE Main 2022 Solution View → 91

A circle touches both the y -axis and the line x + y = 0 . Then the locus of its center

JEE Main 2022 Solution View → 92

Let a circle C touch the lines L _ 1 : 4x - 3y + K _ 1 = 0 and L _ 2 : 4x - 3y + K _ 2 = 0, K _ 1 , K _ 2 ∈ R . If a line passing through the centre of the circle C intersects L _

JEE Main 2022 Solution View → 93

Let the abscissae of the two points P and Q be the roots of 2 x ^ 2 - rx + p = 0 and the ordinates of P and Q be the roots of x ^ 2 - sx - q = 0 . If the equation of the circle

JEE Main 2022 Solution View → 94

Let a circle C: (x - h) ^ 2 + (y - k) ^ 2 = r ^ 2 , k > 0 , touch the x -axis at (1, 0) . If the line x + y = 0 intersects the circle C at P and Q such that the length of the

JEE Main 2022 Solution View → 95

Let B be the centre of the circle x ^ 2 + y ^ 2 - 2x + 4y + 1 = 0 . Let the tangents at two points P and Q on the circle intersect at the point A ( 3, 1 ) . Then 8((area )/(area

JEE Main 2021 Solution View → 96

If the variable line 3x + 4y = α lies between the two circles ( x - 1 ) ^ 2 + ( y - 1 ) ^ 2 = 1 and ( x - 9 ) ^ 2 + ( y - 1 ) ^ 2 = 4, without intercepting a chord on either

JEE Main 2021 Solution View → 97

Two circles each of radius 5 units touch each other at the point ( 1, 2 ) . If the equation of their common tangent is 4x + 3y = 10 , and C _ 1 ( α, β ) and C _ 2 ( γ, δ ) , C _ 1

JEE Main 2021 Solution View → 98

Let the equation x ^ 2 + y ^ 2 + px + ( 1 - p ) y + 5 = 0 represent circles of varying radius r ∈ ( 0, 5 ] . Then the number of elements in the set S = q: q = p ^ 2 and q is an

JEE Main 2021 Solution View → 99

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C _ 1 : x ^ 2 + y ^ 2 + 2y - 5 = 0 at two points P and Q such that PQ is a diameter of C _ 1 .

JEE Main 2021 Solution View → 100

The locus of a point, which moves such that the sum of squares of its distances from the points ( 0, 0 ) , ( 1, 0 ) , ( 0, 1 ) ( 1, 1 ) is 18 units, is a circle of diameter d .

JEE Main 2021 Solution View → 101

Consider a circle C which touches the y - axis at (0, 6) and cuts off an intercept 6 5 on the x - axis. Then the radius of the circle C is equal to :

JEE Main 2021 Solution View → 102

Two tangents are drawn from the point P(- 1, 1) to the circle x ^ 2 + y ^ 2 - 2x - 6y + 6 = 0 . If these tangents touch the circle at points A and B, and if D is a point on the

JEE Main 2021 Solution View → 103

Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through originO . If OC is perpendicular to both the line segments CP and CQ,then the

JEE Main 2021 Solution View → 104

Let A = \ (x, y) ∈ R × R ∣ 2 x ^ 2 + 2 y ^ 2 - 2x - 2y = 1\ B = \ (x, y) ∈ R × R ∣ 4 x ^ 2 + 4 y ^ 2 - 16y + 7 = 0\ and C = \ (x, y) ∈ R × R ∣ x ^ 2 + y ^ 2 - 4x - 2y + 5 ≤ r ^ 2

JEE Main 2021 Solution View → 105

Let the circle S: 36 x ^ 2 + 36 y ^ 2 - 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x - 2y

JEE Main 2021 Solution View → 106

Let r _ 1 and r _ 2 be the radii of the largest and smallest circles, respectively, which pass through the point ( - 4, 1 ) and having their centres on the circumference of the

JEE Main 2021 Solution View → 107

Let S _ 1 : x ^ 2 + y ^ 2 = 9 and S _ 2 : ( x - 2 ) ^ 2 + y ^ 2 = 1 . Then the locus of center of a variable circle S which touches S _ 1 internally and S _ 2 externally always

JEE Main 2021 Solution View → 108

Choose the correct statement about two circles whose equations are given below: x ^ 2 + y ^ 2 - 10x - 10y + 41 = 0 x ^ 2 + y ^ 2 - 22x - 10y + 137 = 0

JEE Main 2021 Solution View → 109

For the four circles M, N, O and P, following four equations are given: Circle M: x ^ 2 + y ^ 2 = 1 Circle N: x ^ 2 + y ^ 2 - 2x = 0 Circle O: x ^ 2 + y ^ 2 - 2x - 2y + 1 = 0

JEE Main 2021 Solution View → 110

Two tangents are drawn from a point P to the circle x ^ 2 + y ^ 2 - 2x - 4y + 4 = 0 , such that the angle between these tangents is ^ - 1 ((12)/(5)) , where ^ - 1 ((12)/(5)) ∈ (

JEE Main 2021 Solution View → 111

Let the tangent to the circle x ^ 2 + y ^ 2 = 25 at the point R ( 3, 4 ) meet x -axis and y -axis at point P and Q , respectively. If r is the radius of the circle passing through

JEE Main 2021 Solution View → 112

The line 2x - y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x - 2y = 4 . Then, the radius of the circle is:

JEE Main 2021 Solution View → 113

Choose the incorrect statement about the two circles whose equations are given below: x ^ 2 + y ^ 2 - 10x - 10y + 41 = 0 and x ^ 2 + y ^ 2 - 16x - 10y + 80 = 0

JEE Main 2021 Solution View → 114

The minimum distance between any two points P _ 1 and P _ 2 while considering point P _ 1 on one circle and point P _ 2 on the other circle for the given circles&#39; equations x

JEE Main 2021 Solution View → 115

Let the lengths of intercepts on x -axis and y -axis made by the circle x ^ 2 + y ^ 2 + ax + 2ay + c = 0, (a < 0) be 2 2 and 2 5 , respectively. Then the shortest distance from

JEE Main 2021 Solution View → 116

Let ABCD be a square of side of unit length. Let a circle C _ 1 centered at A with unit radius is drawn. Another circle C _ 2 which touches C _ 1 and the lines AD and AB are

JEE Main 2021 Solution View → 117

If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x ^ 2 + y ^ 2 = 1 is a circle of radius r , then r is equal to

JEE Main 2021 Solution View → 118

Let A(1, 4) and B(1, - 5) be two points. Let P be a point on the circle ((x - 1)) ^ 2 + (y - 1) ^ 2 = 1 , such that (PA) ^ 2 + (PB) ^ 2 have maximum value, then the points, P, A

JEE Main 2021 Solution View → 119

In the circle given below, let OA = 1 unit, OB = 13 unit and PQ ⊥ OB . Then, the area of the triangle PQB (in square units) is :

JEE Main 2021 Solution View → 120

If one of the diameters of the circle x ^ 2 + y ^ 2 - 2x - 6y + 6 = 0 is a chord of another circle C ' ' , whose center is at (2, 1) , then its radius is_____.

JEE Main 2021 Solution View → 121

If the length of the chord of the circle, x ^ 2 + y ^ 2 = r ^ 2 ( r > 0 ) along the line, y - 2x = 3 is r , then r ^ 2 is equal to:

JEE Main 2020 Solution View → 122

The circle passing through the intersection of the circles, x ^ 2 + y ^ 2 - 6x = 0 and x ^ 2 + y ^ 2 - 4y = 0 having its centre on the line, 2x - 3y + 12 = 0 , also passes through

JEE Main 2020 Solution View → 123

The diameter of the circle, whose Centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2 is

JEE Main 2020 Solution View → 124

The numbers of integral values of k for which the line, 3x + 4y = k intersects the circle, x ^ 2 + y ^ 2 - 2x - 4y + 4 = 0 at two distinct points is....

JEE Main 2020 Solution View → 125

A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0) . Which of the following lines is not a tangent to this circle?

JEE Main 2020 Solution View → 126

If a line y = mx + c , is a tangent to the circle (x - 3) ^ 2 + y ^ 2 = 1 , and it is perpendicular to a line L _ 1 , where L _ 1 is the tangent to the circle x ^ 2 + y ^ 2 = 1

JEE Main 2020 Solution View → 127

Let the tangents drawn from the origin to the circle, x ^ 2 + y ^ 2 - 8x - 4y + 16 = 0 touch it at the points A and B . Then (AB) ^ 2 is equal to

JEE Main 2020 Solution View → 128

Let the circles C _ 1 : x ^ 2 + y ^ 2 = 9 and C _ 2 : (x - 3) ^ 2 + (y - 4) ^ 2 = 16, intersect at the points X and Y . Suppose that another circle C _ 3 : (x - h) ^ 2 + (y - k) ^

JEE Advanced 2019 Solution View → 129

Let the circles C _ 1 : x ^ 2 + y ^ 2 = 9 and C _ 2 : (x - 3) ^ 2 + (y - 4) ^ 2 = 16, intersect at the points X and Y . Suppose that another circle C _ 3 : (x - h) ^ 2 + (y - k) ^

JEE Advanced 2019 Solution View → 130

A line y = mx + 1 intersects the circle (x - 3) ^ 2 + (y + 2) ^ 2 = 25 at the points P and Q . If the midpoint of the line segment PQ has x - coordinate - (3)/(5), then which one

JEE Advanced 2019 Solution View → 131

A circle touching the x - axis at ( 3, 0 ) and making an intercept of length 8 on the y - axis passes through the point:

JEE Main 2019 Solution View → 132

If the angle of intersection at a point where the two circles with radii 5cm and 12cm intersect is 90 ° , then the length (in cm) of their common chord is:

JEE Main 2019 Solution View → 133

The locus of the centres of the circles, which touch the circle, x ^ 2 + y ^ 2 = 1 externally, also touch the y -axis and lie in the first quadrant, is:

JEE Main 2019 Solution View → 134

The line x = y touches a circle at the point ( 1, 1 ) . If the circle also passes through the point ( 1, - 3 ) , then its radius is

JEE Main 2019 Solution View → 135

If the circles x ^ 2 + y ^ 2 + 5Kx + 2y + K = 0 and 2( x ^ 2 + y ^ 2 ) + 2Kx + 3y - 1 = 0, (K ∈ R) , intersect at the points P and Q, then the line 4x + 5y - K = 0 , passes

JEE Main 2019 Solution View → 136

A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7 . If the two adjacent vertices of the rectangle are (- 8, 5) and (6, 5), then the area of the

JEE Main 2019 Solution View → 137

The common tangent to the circles x ^ 2 + y ^ 2 = 4 and x ^ 2 + y ^ 2 + 6x + 8y - 24 = 0 also passes through the point:

JEE Main 2019 Solution View → 138

If a tangent to the circle x ^ 2 + y ^ 2 = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is:

JEE Main 2019 Solution View → 139

The tangent and the normal lines at the point ( 3 , 1) to the circle x ^ 2 + y ^ 2 = 4 and the x -axis form a triangle. The area of this triangle (in square units) is:

JEE Main 2019 Solution View → 140

The sum of the squares of the lengths of the chords intercepted on the circle, x ^ 2 + y ^ 2 = 16, by the lines, x + y = n, n ∈ N, where N is the set of all natural numbers is:

JEE Main 2019 Solution View → 141

If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B , then the locus of the foot of perpendicular from O on AB is :

JEE Main 2019 Solution View → 142

Let C _ 1 and C _ 2 be the centres of the circles x ^ 2 + y ^ 2 - 2x - 2y - 2 = 0 and x ^ 2 + y ^ 2 - 6x - 6y + 14 = 0 respectively. If P and Q are the points of intersection of

JEE Main 2019 Solution View → 143

If a variable line 3x + 4y - λ = 0 is such that the two circles x ^ 2 + y ^ 2 - 2x - 2y + 1 = 0 and x ^ 2 + y ^ 2 - 18x - 2y + 78 = 0 are on its opposite sides, then the set of

JEE Main 2019 Solution View → 144

A circle cuts a chord of length 4 a on the x -axis and passes through a point on the y -axis, distant 2 ~b from the origin. Then the locus of the centre of this circle, is:

JEE Main 2019 Solution View → 145

A square is inscribed in the circle x^ 2 +y^ 2 -6 x+8 y-103=0 with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to

JEE Main 2019 Solution View → 146

Two circles with equal radii are intersecting at the points (0,1) and (0,-1) . The tangent at the point (0,1) to one of the circles passes through the centre of the other circle.

JEE Main 2019 Solution View → 147

The straight line x+2 y=1 meets the coordinate axes at A and B . A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent

JEE Main 2019 Solution View → 148

If the area of an equilateral triangle inscribed in the circle x ^ 2 + y ^ 2 + 10x + 12y + c = 0 is 27 3 sq . units, then c is equal to:

JEE Main 2019 Solution View → 149

If a circle C passing through the point (4, 0) touches the circle x ^ 2 + y ^ 2 + 4x - 6y = 12 externally at the point (1, - 1), then the radius of C is:

JEE Main 2019 Solution View → 150

If the circles x ^ 2 + y ^ 2 - 16x - 20y + 164 = r ^ 2 and ( x - 4 ) ^ 2 + (y - 7) ^ 2 = 36 intersect at two distinct points, then:

JEE Main 2019 Solution View → 151

Three circles of radii a, b, c, (a < b < c) touch each other externally. If they have x - axis as a common tangent, then:

JEE Main 2019 Solution View → 152

Let T be the line passing through the points P(- 2, 7) and Q (2, - 5). Let F _ 1 be the set of all pairs of circles ( S _ 1 , S _ 2 ) such that T is tangents to S _ 1 at P and

JEE Advanced 2018 Solution View → 153

Paragraph: Let S be the circle in the xy &ndash; plane defined by the equation x ^ 2 + y ^ 2 = 4 . Question : Let E _ 1 E _ 2 and F _ 1 F _ 2 be the chords of S passing through

JEE Advanced 2018 Solution View → 154

Paragraph: Let S be the circle in the xy &ndash; plane defined by the equation x ^ 2 + y ^ 2 = 4 . Question : Let P be a point on the circle S with both coordinates being

JEE Advanced 2018 Solution View → 155

If a circle C , whose radius is 3 , touches externally the circle x ^ 2 + y ^ 2 + 2x - 4y - 4 = 0 at the point (2, 2) , then the length of the intercept cut by this circle C on

JEE Main 2018 Solution View → 156

The tangent to the circle C_1: x^2+y^2-2 x-1=0 at the point (2,1) cuts off a chord of length 4 from a circle C_2 whose centre is (3,-2) . The radius of C_2 is

JEE Main 2018 Solution View → 157

A circle passes through the points (2,3) and (4 , 5). If its centre lies on the line, y-4 x+3=0 , then its radius is equal to

JEE Main 2018 Solution View → 158

A circle passes through the points (2, 3) and (4, 5) . If its centre lies on the line y - 4x + 3 = 0 , then its radius is equal to :

JEE Main 2018 Solution View → 159

For how many values of p , the circle x ^ 2 + y ^ 2 + 2x + 4y - p = 0 and the coordinate axes have exactly three common points?

JEE Advanced 2017 Solution View → 160

A line drawn through the point P(4, 7) cuts the circle x ^ 2 + y ^ 2 = 9 at the points A and B . Then P _ A · P _ B is equal to.

JEE Main 2017 Solution View → 161

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles ^ - 1 ⁡ ((1)/(7)) and sec ^ - 1 ⁡ (7) at the center

JEE Main 2017 Solution View → 162

If the common tangents to the parabola, x ^ 2 = 4y and the circle, x ^ 2 + y ^ 2 = 4 intersect at the point P , then the distance of P from the origin (units), is:

JEE Main 2017 Solution View → 163

If a point P(0, - 2) and Q is any point on the circle, x ^ 2 + y ^ 2 - 5x - y + 5 = 0 , then the maximum value of (PQ) ^ 2 is

JEE Main 2017 Solution View → 164

The radius of a circle, having minimum area, which touches the curve y = 4 - x ^ 2 and the lines, y = |x| is:

JEE Main 2017 Solution View → 165

Let RS be the diameter of the circle x ^ 2 + y ^ 2 = 1 where, S is the point ( 1, 0 ) . Let P be a variable point (other than R and S ) on the circle and tangents to the circle at

JEE Advanced 2016 Solution View → 166

The circle C _ 1 : x ^ 2 + y ^ 2 = 3, with centre at O, intersects the parabola x ^ 2 = 2y at the point P in the first quadrant. Let the tangent to the circle C _ 1 at P touches

JEE Advanced 2016 Solution View → 167

Equation of the tangent to the circle, at the point (1, - 1) , whose center, is the point of intersection of the straight lines x - y = 1 and 2x + y = 3 is:

JEE Main 2016 Solution View → 168

A circle passes through (- 2, 4) and touches the y - axis at (0, 2) . Which one of the following equations can represent a diameter of this circle ?

JEE Main 2016 Solution View → 169

The centres of those circles which touch the circle, x ^ 2 + y ^ 2 - 8x - 8y - 4 = 0, externally and also touch the x - axis, lie on

JEE Main 2016 Solution View → 170

If one of the diameters of the circle, given by the equation, x ^ 2 + y ^ 2 - 4x + 6y - 12 = 0, is a chord of a circle S , whose centre is at (- 3, 2) , then the radius of S is

JEE Main 2016 Solution View → 171

If a circle passing through the point (- 1, 0) touches y -axis at (0, 2) , then the x -intercept of the circle is

JEE Main 2015 Solution View → 172

If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0 , then the equation of the circumcircle of this triangle is:

JEE Main 2015 Solution View → 173

If y + 3x = 0 is the equation of a chord of the circle x ^ 2 + y ^ 2 - 30x = 0 , then the equation of the circle with this chord as diameter is :

JEE Main 2015 Solution View → 174

Let the tangents drawn to the circle, x ^ 2 + y ^ 2 = 16 from the point P(0, h) meet the x -axis at points A and B . If the area of is minimum, then positive value of h is:

JEE Main 2015 Solution View → 175

The number of common tangents to the circles x ^ 2 + y ^ 2 - 4 x - 6 y - 1 2 = 0 and x ^ 2 + y ^ 2 + 6x + 18y + 26 = 0 , is

JEE Main 2015 Solution View → 176

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1) ^ 2 + y ^ 2 = 16 and x ⁡ ^ 2 + y ⁡ ^ 2 = 1 . Then

JEE Advanced 2014 Solution View → 177

The equation of the circle described on the chord 3x ⁡ + y ⁡ + 5 = 0 of the circle x ⁡ ^ 2 + y ⁡ ^ 2 = 16 as the diameter is

JEE Main 2014 Solution View → 178

For the two circles x^2+y^2=16 and x^2+y^2-2 y=0 , there is/are

JEE Main 2014 Solution View → 179

The set of all real values of λ for which exactly two common tangents can be drawn to the circles x^2+y^2-4 x-4 y+6=0 and x^2+y^2-10 x-10 y+λ=0 is the interval:

JEE Main 2014 Solution View → 180

Let L_1 be the length of the common chord of the curves x^2+y^2=9 and y^2=8 x , and L_2 be the length of the latus rectum of y^2=8 x , then:

JEE Main 2014 Solution View → 181

If the point (1, 4) lies inside the circle x ^ 2 + y ^ 2 - 6x + 10y + p = 0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of

JEE Main 2014 Solution View → 182

Let C be the circle with center at (1, 1) and radius = 1 . If T is the circle centered at (0, y) , passing through the origin and touching the circle C externally, then the radius

JEE Main 2014 Solution View → 183

Circle(s) touching x -axis at a distance 3 from the origin and having an intercept of length 2 7 on y -axis is (are)

JEE Advanced 2013 Solution View → 184

Statement 1: The only circle having radius 10 and a diameter along line 2 x+y=5 is x^2+y^2-6 x +2 y=0 . Statement 2: 2 x+y=5 is a normal to the circle x^2+y^2-6 x+2 y=0 .

JEE Main 2013 Solution View → 185

If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle 60^ ∘ on the circumference of the first circle, then the radius of the arc is:

JEE Main 2013 Solution View → 186

If the circle x^2+y^2-6 x-8 y+(25-a^2)=0 touches the axis of x , then a equals.

JEE Main 2013 Solution View → 187

If a circle C passing through (4,0) touches the circle x^2+y^2+4 x-6 y-12=0 externally at a point (1,-1) , then the radius of the circle C is :

JEE Main 2013 Solution View → 188

If each of the lines 5 x+8 y=13 and 4 x-y=3 contains a diameter of the circle x^2+y^2-2(a^2-7 a+11) x-2(a^2-6 a+6) y+b^3+1=0 , then :

JEE Main 2013 Solution View → 189

The circle passing through ( 1, - 2 ) and touching the axis of x at ( 3, 0 ) also passes through the point

JEE Main 2013 Solution View → 190

Given : A circle, 2 x ^ 2 + 2 y ^ 2 = 5 and a parabola, y ^ 2 = 4 5 x . Statement - I : An equation of a common tangent to these curves is y = x + 5 . Statement - II : If the

JEE Main 2013 Solution View → 191

A tangent P T is drawn to the circle x^ 2 +y^ 2 =4 at the point P( 3 , 1) . A straight line L , perpendicular to P T is a tangent to the circle (x-3)^ 2 +y^ 2 -1 . Question: A

JEE Advanced 2012 Solution View → 192

A tangent P T is drawn to the circle x^ 2 +y^ 2 =4 at the point P( 3 , 1) . A straight line L , perpendicular to P T is a tangent to the circle (x-3)^ 2 +y^ 2 -1 . Question: A

JEE Advanced 2012 Solution View → 193

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4 x- 5 y=20 to the circle x^ 2 +y^ 2 =9 is

JEE Advanced 2012 Solution View → 194

The number of common tangents of the circles given by x^2+y^2-8 x-2 y+1=0 and x^2+y^2+6 x+8 y=0 is

JEE Main 2012 Solution View → 195

If the line y=m x+1 meets the circle x^2+y^2+3 x=0 in two points equidistant from and on opposite sides of x -axis, then

JEE Main 2012 Solution View → 196

The equation of the circle passing through the point (1,2) and through the points of intersection of x^2+y^2-4 x-6 y-21=0 and 3 x+4 y+5=0 is given by

JEE Main 2012 Solution View → 197

The length of the diameter of the circle which touches the x -axis at the point (1,0) and passes through the point (2,3) is

JEE Main 2012 Solution View → 198

The circle passing through the point (-1,0) and touching the Y -axis at (0,2) , also passes through the point

JEE Advanced 2011 Solution View → 199

The straight line 2 x-3 y=1 divides the circular region x^2+y^2 ≤ 6 into two parts. If S=\ (2, (3)/(4)),((5)/(2), (3)/(4)),((1)/(4),-(1)/(4)),((1)/(8), (1)/(4))\ , then the number

JEE Advanced 2011 Solution View → 200

The two circles x^2+y^2=a x and x^2+y^2=c^2(c>0) touch each other if

JEE Main 2011 Solution View →
Practice all Circle questions in the app →

Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Circle in other exams

BITSAT Circle (27)