JEE MAIN · MATHEMATICS · CIRCLES
JEE Main Circles Questions & Solutions
40 solved questions on Circles, ranging from easy to JEE-Advanced-flavour hard. Click any to see the full solution.
40 solved questions on Circles, ranging from easy to JEE-Advanced-flavour hard. Click any to see the full solution.
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 :
View solution →Choose the correct statement about two circles whose equations are given below :x2 + y2 $-$ 10x $-$ 10y + 41 = 0x2 + y2 $-$ 22x $-$ 10y + 137 = 0
View solution →Let S1 : x2 + y2 = 9 and S2 : (x $-$ 2)2 + y2 = 1. Then the locus of center of a variable circle S which touches S1 internally and S2 externally always passes through the points :
View solution →A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y $-$ 5 = 0 at two points P and Q such that PQ is a diameter of C1. Then the…
View solution →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…
View solution →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. Then d2 is…
View solution →Let the locus of the midpoints of the chords of the circle $x^2+(y-1)^2=1$ drawn from the origin intersect the line $x+y=1$ at $\mathrm{P}$ and $\mathrm{Q}$. Then, the length of…
View solution →Let a circle passing through $(2,0)$ have its centre at the point $(\mathrm{h}, \mathrm{k})$. Let $(x_{\mathrm{c}}, y_{\mathrm{c}})$ be the point of intersection of the lines $3…
View solution →Let the mirror image of a circle $c_{1}: x^{2}+y^{2}-2 x-6 y+\alpha=0$ in line $y=x+1$ be $c_{2}: 5 x^{2}+5 y^{2}+10 g x+10 f y+38=0$. If $\mathrm{r}$ is the radius of circle…
View solution →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…
View solution →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 $\mathrm{T}$ to it at the point $(3,2)$. Let $C_{2}$ be the image…
View solution →If the curves, x2 – 6x + y2 + 8 = 0 and x2 – 8y + y2 + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is ______.
View solution →Let the lines $y + 2x = \sqrt {11} + 7\sqrt 7$ and $2y + x = 2\sqrt {11} + 6\sqrt 7$ be normal to a circle $C:{(x - h)^2} + {(y - k)^2} = {r^2}$. If the line $\sqrt {11} y - 3x =…
View solution →Let the equation x2 + y2 + px + (1 $-$ p)y + 5 = 0 represent circles of varying radius r $\in$ (0, 5]. Then the number of elements in the set S = {q : q = p2 and q is an integer}…
View solution →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 $\mathrm{P}$ and $\mathrm{Q}$ be the roots of $y^{2}+2 y-7=0$. If…
View solution →If a line, y = mx + c is a tangent to the circle, (x – 3)2 + y2 = 1 and it is perpendicular to a line L1, where L1 is the tangent to the circle, x2 + y2 = 1 at the point $\left(…
View solution →If the image of the point $(-4,5)$ in the line $x+2 y=2$ lies on the circle $(x+4)^2+(y-3)^2=r^2$, then $r$ is equal to:
View solution →Choose the incorrect statement about the two circles whose equations are given below :x2 + y2 $-$ 10x $-$ 10y + 41 = 0 and x2 + y2 $-$ 16x $-$ 10y + 80 = 0
View solution →Let C be a circle passing through the points A(2, $-$1) and B(3, 4). The line segment AB s not a diameter of C. If r is the radius of C and its centre lies on the circle ${(x -…
View solution →The circle passing through the intersection of the circles, x2 + y2 – 6x = 0 and x2 + y2 – 4y = 0, having its centre on the line, 2x – 3y + 12 = 0, also passes through the…
View solution →If the circles ${x^2} + {y^2} + 6x + 8y + 16 = 0$ and $${x^2} + {y^2} + 2\left( {3 - \sqrt 3 } \right)x + 2\left( {4 - \sqrt 6 } \right)y = k + 6\sqrt 3 + 8\sqrt 6 $$, $k 0$,…
View solution →A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is :
View solution →Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2${\sqrt 2 }$ and 2${\sqrt 5 }$, respectively. Then the shortest…
View solution →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 $S(\alpha,\beta)$, then…
View solution →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 and B lie on…
View solution →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 $\left( {1, - {1 \over 3}} \right)$ lies on or…
View solution →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 points $A$ and $B$. Then the minimum value of $O A+O…
View solution →Consider a circle $C_{1}: x^{2}+y^{2}-4 x-2 y=\alpha-5$. Let its mirror image in the line $y=2 x+1$ be another circle $C_{2}: 5 x^{2}+5 y^{2}-10 f x-10 g y+36=0$. Let $r$ be the…
View solution →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 the point…
View solution →The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x2 + y2 – 2x – 4y + 4 = 0 at two distinct points is ______.
View solution →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
View solution →If one of the diameters of the circle ${x^2} + {y^2} - 2\sqrt 2 x - 6\sqrt 2 y + 14 = 0$ is a chord of the circle ${(x - 2\sqrt 2 )^2} + {(y - 2\sqrt 2 )^2} = {r^2}$, then the…
View solution →Let the point $(p, p+1)$ lie inside the region $E=\left\{(x, y): 3-x \leq y \leq \sqrt{9-x^{2}}, 0 \leq x \leq 3\right\}$. If the set of all values of $\mathrm{p}$ is the interval…
View solution →Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $\mathrm{C_2}$ be a circle having centre at $(-1,0)$ and radius 2 . If the line of the common chord of $\mathrm{C}_1$ and…
View solution →If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x $-$ 2)2 + (y $-$ 3)2 = 25 at the point (5, 7) is A, then 24A is equal to…
View solution →If the circle $x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R}$ passes through the point $(6,1)$ and its centre lies on the line $x-2 c y=8$, then the length of intercept made…
View solution →Let PQ be a diameter of the circle x2 + y2 = 9. If $\alpha$ and $\beta$ are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the…
View solution →Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point ($-$5, 0). If the locus of the point P is a circle of radius r, then 4r2…
View solution →If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of radius r, then r is equal to :
View solution →Let $C: x^2+y^2=4$ and $C^{\prime}: x^2+y^2-4 \lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles $\mathrm{C}$ and $\mathrm{C}$ intersect at…
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