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Circle — JEE Main & Advanced Mathematics PYQs

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

506 questionsMathematicsSolutions on every page
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 th

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( , ) is a point on C such that PQ = PR , then (6 + 8 )^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 circl

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 p

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 x²+y²=4 intersect x -axis at the points A ( a , 0), a >0 and B ( b , 0) . Let P (2 , 2 ) , 0< < 2 and Q (2 , 2 ) be two points such that ( - )= 2 . Then the point of

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 given cho

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 x²+2 y²-6 x-12 y+23=0 and 4 x²+2 y²-20 x-12 y+35=0 lie on a circle of radius r and centre (a, b) , then the value of a b+18 r² is

JEE Main 2026 Solution View → 15

Let the set of all values of r , for which the circles (x+1)²+(y+4)²=r² and x²+y²-4 x-2 y-4=0 intersect at two distinct points be the interval ( , ) . Then is equal to

JEE Main 2026 Solution View → 16

If P is a point on the circle x²+y²=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 such po

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 ₁, ₂ ( ₁> ₂ ) are the possible values of ( c + d ) (-7 i +2 j +3 k ) , then the equati

JEE Main 2026 Solution View → 18

Let PQ and MN be two straight lines touching the circle x²+y²-4 x-6 y-3=0 at the points A and B respectively. Let O be the centre of the circle and AOB = / 3 . Then the locus of th

JEE Main 2026 Solution View → 19

Let C₁ 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 ( , ) .

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 the

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- x+ y+ =0 . If the circle lies below x -a

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 centr

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 , and O

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 circl

JEE Main 2025 Solution View → 28

Let the straight line y =2 x touch a circle with center (0, ), >0 , and radius r at a point A ₁ . Let B ₁ be the point on the circle such that the line segment A₁ B₁ is a diameter

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 1 x_

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 (h,

JEE Main 2024 Solution View → 31

Let the circles C₁:(x- )^2+(y- )^2=r₁^2 and C₂:(x-8)^2+ (y- 15 2 )^2=r₂^2 touch each other externally at the point (6,6) . If the point (6,6) divides the line segment joining the c

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 e

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 circl

JEE Main 2024 Solution View → 35

Let the circle C₁: x^2+y^2-2(x+y)+1=0 and C₂ 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 point P

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 slop

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 (x_i^2+y_i^2 ) is equ

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 P Q is:

JEE Main 2024 Solution View → 40

Let 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 ' intersect at two distinct points, is R − a , b

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 = 2 y . Let the line L touch two c

JEE Main 2024 Solution View → 42

Let 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 and B . Then the minimum value of O A +

JEE Main 2024 Solution View → 43

If 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 intersection of the lines 2 x + 3 y = 12 and 3 x

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 one of the in

JEE Main 2024 Solution View → 45

If 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, then

JEE Main 2024 Solution View → 46

Equations 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 intersects the circle at only one point P ( α ,

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 + β ) 2 is e

JEE Main 2024 Solution View → 48

Four distinct points ( 2 k , 3 k ) , ( 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 &#60; r &#60; 3 . Two distinct commo

JEE Advanced 2023 Solution View → 50

The 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 , is

JEE Main 2023 Solution View → 51

Let the centre of a circle C be &#945; , &#946; and its radius r &#60; 8 . Let 3 x + 4 y = 24 and 3 x &#8211; 4 y = 32 be two tangents and 4 x + 3 y = 1 be a normal to C . Then ( &

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 2 2 - r 1 r

JEE Main 2023 Solution View → 53

Consider ellipses E k : k x 2 + k 2 y 2 = 1 , k = 1 , 2 , &#8230; , 20 . Let C k be the circle which touches the four chords joining the end points (one on minor axis and another o

JEE Main 2023 Solution View → 54

Let A be 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 A B in the ratio 3 : 2 is the p

JEE Main 2023 Solution View → 55

A line segment A B of length &#955; moves such that the points A and B remain on the periphery of a circle of radius &#955; . Then the locus of the point, that divides the line seg

JEE Main 2023 Solution View → 56

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

JEE Main 2023 Solution View → 57

Consider a circle C 1 &#160; : &#160; x &#160; 2 + y 2 &#160; &#8211; &#160; 4 x &#160; &#8211; &#160; 2 y &#160; = &#160; &#945; &#160; &#8211; &#160; 5 . Let its mirror image in

JEE Main 2023 Solution View → 58

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

JEE Main 2023 Solution View → 59

A circle passing through the point P &#945; , &#946; in the first quadrant touches the two coordinate axes at the points A and B . The point P is above the line A B . The point Q o

JEE Main 2023 Solution View → 60

Let the point p , p + 1 lie inside the region E = x , y : 3 - x &#8804; y &#8804; 9 - x 2 , 0 &#8804; x &#8804; 3 . If the set of all values of p is the interval a , b , then b 2 +

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 ) x - ( 1 - a ) y

JEE Main 2023 Solution View → 62

Let a circle C 1 be obtained on rolling the circle x 2 + y 2 - 4 x - 6 y + 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 in T . Let

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 O C be perpendicular to both C P and C Q . If the area of the t

JEE Main 2023 Solution View → 64

Let y = x + 2 , 4 y = 3 x + 6 and 3 y = 4 x + 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 ( &#945; , &#946; ) , then 4 &

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 - 3 x + 10 y - 15 = 0 , intersect at the point C . Then the radius of the circle, whose cent

JEE Main 2023 Solution View → 67

Points P - 3 , 2 , Q 9 , 10 and R &#945; , 4 lie on a circle C with P R as its diameter. The tangents to C at the points Q and R intersect at the point S . If S lies on the line 2

JEE Main 2023 Solution View → 68

The points of intersection of the line a x + b y = 0 , ( a &#8800; b ) and the circle x 2 + y 2 - 2 x = 0 are A ( &#945; , 0 ) and B ( 1 , &#946; ) . The image of the circle with A

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 &#952; i at the centre of the circle C i , is a circle of radius r i .

JEE Main 2023 Solution View → 70

Let G be a circle of radius R &#62; 0 . Let G 1 , G 2 , &#8230; , G n be n circles of equal radius r &#62; 0 . Suppose each of the n circles G 1 , G 2 , &#8230; , G n touches the c

JEE Advanced 2022 Solution View → 71

Let A B 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 distance of

JEE Main 2022 Solution View → 72

Let a line L pass through the point of intersection of the lines b x + 10 y - 8 = 0 and 2 x - 3 y = 0 , b &#8712; R - 4 3 . If the line L also passes through the point 1 , 1 and to

JEE Main 2022 Solution View → 73

Let the mirror image of a circle c 1 : x 2 + y 2 - 2 x - 6 y + &#945; = 0 in line y = x + 1 be c 2 : 5 x 2 + 5 y 2 + 10 g x + 10 f y + 38 = 0 . If r is the radius of circle c 2 , t

JEE Main 2022 Solution View → 74

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

JEE Main 2022 Solution View → 75

Let C be the centre of the circle x 2 + y 2 - x + 2 y = 11 4 and P be a point on the circle. A line passes through the point C , makes an angle of &#960; 4 with the line C P and in

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 = 2 x gives a chord O A of a circle C 1 . Let C 2 be the circle with O A as a diamet

JEE Main 2022 Solution View → 77

If the circle x 2 + y 2 - 2 g x + 6 y - 19 c = 0 , g , c &#8712; &#8477; passes through the point 6 , 1 and its centre lies on the line x - 2 c y = 8 , then the length of intercept

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 - 4 x - 6 = 0 and the ordinates of P and Q be the roots of y 2 + 2 y - 7 = 0 . If P Q is a diameter of t

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 points

JEE Main 2022 Solution View → 80

If the circles x 2 + y 2 + 6 x + 8 y + 16 = 0 and x 2 + y 2 + 2 3 - 3 x + 2 4 - 6 y = k + 6 3 + 8 6 , k &#62; 0 , touch internally at the point P &#945; , &#946; , then &#945; + 3

JEE Main 2022 Solution View → 81

Let the locus of the centre &#945; , &#946; , &#946; &#62; 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

JEE Main 2022 Solution View → 82

Let a triangle A B C be inscribed in the circle x 2 - 2 x + y + y 2 = 0 such that &#8736; B A C = &#960; 2 . If the length of side A B is 2 , then the area of the &#9651; A B C is

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 tangents to C 2

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 - 2 x - 4 y = 0 intersect at the point Q , then the area of the triangle O P Q is equal to

JEE Main 2022 Solution View → 86

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

JEE Main 2022 Solution View → 87

The set of values of k for which the circle C : 4 x 2 + 4 y 2 - 12 x + 8 y + 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 = 4 x + 3 y + 2 passes through the centre P of the circle C and intersects the line L 2 : 3 x - 4 y - 11 = 0 at Q . T

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 2 x - y + 4 = 0 , then the area of

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 A B is not a diameter of C . If r is the radius of C and its centre lies on the circle x - 5 2

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 : 4 x - 3 y + K 1 = 0 and L 2 : 4 x - 3 y + K 2 = 0 , K 1 , K 2 &#8712; R . If a line passing through the centre of the circle C intersects L 1 a

JEE Main 2022 Solution View → 93

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

JEE Main 2022 Solution View → 94

Let a circle C : x - h 2 + y - k 2 = r 2 , k &#62; 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 chord P Q i

JEE Main 2022 Solution View → 95

Let B be the centre of the circle x 2 + y 2 - 2 x + 4 y + 1 = 0 . Let the tangents at two points P and Q on the circle intersect at the point A ( 3 , 1 ) . Then 8 area &#916; APQ a

JEE Main 2021 Solution View → 96

If the variable line 3 x + 4 y = &#945; 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 circle

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 4 x + 3 y = 10 , and C 1 ( &#945; , &#946; ) and C 2 ( &#947

JEE Main 2021 Solution View → 98

Let the equation x 2 + y 2 + p x + ( 1 - p ) y + 5 = 0 represent circles of varying radius r &#8712; ( 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 = 2 y at the point 2 , 1 and intersects the circle C 1 : x 2 + y 2 + 2 y - 5 = 0 at two points P and Q such that P Q is a diameter of C 1 . Then the d

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 - 2 x - 6 y + 6 = 0 . If these tangents touch the circle at points A and B , and if D is a point on the circ

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 origin O . If O C is perpendicular to both the line segments C P and C Q , then

JEE Main 2021 Solution View → 104

Let A = x , y &#8712; R &#215; R &#8739; 2 x 2 + 2 y 2 - 2 x - 2 y = 1 B = x , y &#8712; R &#215; R &#8739; 4 x 2 + 4 y 2 - 16 y + 7 = 0 and C = x , y &#8712; R &#215; R &#8739; x

JEE Main 2021 Solution View → 105

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

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 circle

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 passes through the

JEE Main 2021 Solution View → 108

Choose the correct statement about two circles whose equations are given below: x 2 + y 2 - 10 x - 10 y + 41 = 0 x 2 + y 2 - 22 x - 10 y + 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 - 2 x = 0 Circle O : x 2 + y 2 - 2 x - 2 y + 1 = 0 Circle P

JEE Main 2021 Solution View → 110

Two tangents are drawn from a point P to the circle x 2 + y 2 - 2 x - 4 y + 4 = 0 , such that the angle between these tangents is tan - 1 12 5 , where tan - 1 12 5 &#8712; ( 0 , &#

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 the

JEE Main 2021 Solution View → 112

The line 2 x - y + 1 = 0 is a tangent to the circle at the point 2 , 5 and the centre of the circle lies on x - 2 y = 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 - 10 x - 10 y + 41 = 0 and x 2 + y 2 - 16 x - 10 y + 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 2 + y 2 -

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 + a x + 2 a y + c = 0 , a &#60; 0 be 2 2 and 2 5 , respectively. Then the shortest distance from o

JEE Main 2021 Solution View → 116

Let A B C D 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 A D and A B are tangent

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 P A 2 + P B 2 have maximum value, then the points, P , A and B lie on

JEE Main 2021 Solution View → 119

In the circle given below, let O A = 1 unit, O B = 13 unit and P Q &#8869; O B . Then, the area of the triangle P Q B (in square units) is :

JEE Main 2021 Solution View → 120

If one of the diameters of the circle x 2 + y 2 - 2 x - 6 y + 6 = 0 is a chord of another circle C &#39; &#39; , whose center is at 2 , 1 , then its radius is_____.

JEE Main 2021 Solution View →
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