The tangent to the circle $x^2 + y^2 = 5$ at the point $(1, -2)$ intersects the circle $x^2 + y^2 - 8x + 6y + 20 = 0$ at which of the following?

The point $(3, -4)$ lies on both the circles $x^2 + y^2 - 2x + 8y + 13 = 0$ and $x^2 + y^2 - 4x + 6y + 11 = 0$. Then,the angle between the circles is

$C_1$ and $C_2$ are the external and internal centres of similitude of the circles $x^2+y^2-2x+4y+1=0$ and $x^2+y^2+4x-6y+12=0$. If the radius of the circle having $C_1C_2$ as its diameter is $r$,then $\frac{9}{2}r=$

The equation of the circle having the chord $x - y - 1 = 0$ of the circle $2x^2 + 2y^2 - 2x - 6y - 25 = 0$ as its diameter is:

Find the equation of a circle which cuts the circle $x^2+y^2-6x+4y-3=0$ orthogonally,while passing through $(3,0)$ and touching the $Y$-axis.

Let $a=1+i$ and $z=x+iy$. If the curve $z\bar{z}+az+\bar{a}\bar{z}-4=0$ is cut by the straight line $(z+\bar{z})-i(z-\bar{z})+2=0$ at two points $A$ and $B$, then the equation of the circle passing through the origin, $A$ and $B$ is