List of top Mathematics Questions on Circle asked in JEE Main

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

If one of the diameters of the circle $x^2+y^2-10x+4y+13=0$ is a chord of another circle and whose center is the point of intersection of the lines $2x + 3y = 12$ and $3x - 2y = 5 $ then the radius of the circle is

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

If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to

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 :

The points of intersection of the line $a x+b y=0,(a \neq b)$ and the circle $x^2+y^2-2 x=0$ are $A (\alpha, 0)$ and $B (1, \beta)$ The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is :

The locus of the mid points of the chords of the circle $C_1:(x-4)^2+(y-5)^2=4$ which subtend an angle $\theta_i$ at the centre of the circle $C_1$, is a circle of radius $r_i$ If $\theta_1=\frac{\pi}{3}, \theta_3=\frac{2 \pi}{3}$ and $r_1^2=r_2^2+r_3^2$, then $\theta_2$ is equal to

The distance of the point $(6,-2 \sqrt{2})$ from the common tangent $y=m x+c, m>$, of the curves $x=2 y^2$ and $x=1+y^2$ is :

A circle passing through the point P$( \alpha , \beta )$ 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 segment AB is the foot of perpendicular from P on AB. If PQ is equal to 11 units, then value of $( \alpha \beta )$ is ___

Two circles having radius $r_1$ and $r_2$ touch both the coordinate axes. Line $x+y=2$ makes intercept 2 on both the circles. The value of $r_{1}^{2} + r_{2}^{2} - r_{1}r_{2}$ is:

Let A be the point (1, 2) and B be any point on the curve $ x^2 + y^2 = 16 $. If the centre of the locus of the point P, which divides the line segment AB in the ratio 3:2 is the point C ($ \alpha, \beta $), then the length of the line segment AC is:

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 $ \left( \alpha, \frac{1}{2} \right) $, then a value of $ \alpha $ is.