Relative Positions of Two Circles

The radius of the circle, having centre at (2, 1), whose one of the chord is a diameter of the circle ${\text{x}}^2+{\text{y}}^2-2\text{x}-6\text{y}+6=0$

Check whether the given two circles touch each other, do not touch each other or intersect each other by making a quadratic equation

$x^2+6x+y^2+5y+10=0$

$x^2+4x+y^2+3y+12=0$

Check whether the given two circles touch each other, do not touch each other or intersect each other by making a quadratic equation

$x^2+5x+y^2-4y-9=0$

$x^2+4x+y^2-3y-7=0$

Check whether the given two circles touch each other, do not touch each other or intersect each other by making a quadratic equation

$x^2+4x+y^2+3y+8=0$

$x^2+3x+y^2+4y+10=0$

Check whether the given two circles touch each other, do not touch each other or intersect each other by making a quadratic equation

$x^2-4x+4+y^2-6y+9=9$

$x^2-2x+1+y^2+2y+1=16$

If the circles $x^2+y^2=9$ and $x^2+y^2+2\alpha x+2y+1=0$ touch each other internally, then $\alpha$ is equal to

Find the equation of the circle passing through $(1, 1)$ and the points of intersection of the circles $x^2+y^2+13x-3y=0$ and $2x^2+2y^2+4x-7y-25=0$.

Find the equation of the circle passing through the points of intersection of the circles $x^2+y^2-x+7y-3=0$ and $x^2+y^2-5x-y+1=0$ and with its centre on the line $y+x=0$.

Prove that the two circles $x^2+y^2-4=0$ and $2x^2+2y^2-11=0$ are concentric.

If $S, S_1, S_2$ be the circles of radii $5,3,2$ respectively. If $S_1$ and $S_2$ touch externally and they touch internally with $S.$ The radius of circle $S_3$ which touches externally with $S_1$ and $S_2$ and internally with $S$ is

If two circles pass through $\mathrm{A}(1,0)$ and $\mathrm{B}(2,-1)$ and the y -axis is a common tangent, then find the sum of possible radii.

If the circles $x^2+y^2+(3+\sin \beta )x+\left(2\cos \alpha \right)y=0$ and $x^2+y^2+\left(2\cos \alpha \right)x+2cy=0$ touch each other, then the maximum value of $c$ is lesser than or equal to

The two circles $x^2+y^2=ax$ and $x^2+y^2=c^2 \left(c>0\right)$ touch each other, if $\left|\frac{c}{a}\right|$ is equal to

The circle $x^2+y^2=1$ is completely contained in the circle $x^2+y^2+4x+3y+k=0$, if

Two circles with centre at O and O' and radii 5cm and 2cm respectively as shown in the figure. If AB and CD are two common tangents to both the circles. Then $A{B}^2-C{D}^2$ is equal to :

The number of common tangents to the circles
$x^2+y^2-2x-4y+1=0$ and $x^2+y^2-12x-16y+91=0$, is

The circles $x^2+y^2-10x+16=0$ and $x^2+y^2=r^2$ intersect each other at two distinct points, if

If the circles $x^2+y^2=9$ and $x^2+y^2+2\alpha x+2y+1=0$ touch each other internally, then $\alpha$ is equal to

Tangents drawn from the point $P(1, 8)$ to the circle $x^2+y^2-6x-4y-11=0$ touch the circle at the points $A$and$B$. The equation of the circumcircle of the triangle $PAB$ is

The two circles $x^2+y^2-2x+6y+6=0$ and $x^2+y^2-5x+6y+15=0$ touch each other