If the circle $x^2 + y^2 + 4x + 22y + c = 0$ bisects the circumference of the circle $x^2 + y^2 - 2x + 8y - d = 0$,then $c + d = . . . . .$

The radical axis of the circles $x^2+y^2+5x+4y-5=0$ and $x^2+y^2-3x+5y-6=0$ is:

If one of the diameters of the circle $x^{2}+y^{2}-2x-6y+6=0$ is a chord of another circle $'C'$,whose center is at $(2,1)$,then its radius is..........

If $x-4=0$ is the radical axis of two orthogonal circles,out of which one is $x^2+y^2=36$,then the centre of the other circle is

$P$ is a point of intersection of the circles $S \equiv x^2+y^2-6x+2ky+1=0$ and $S' \equiv x^2+y^2+2kx-6y-7=0$. If the tangent at $P$ to $S=0$ passes through the centre of $S'=0$ and the tangent at $P$ to $S'=0$ passes through the centre of $S=0$,then the radius of $S'=0$ is

Consider the family of circles $x^2+y^2-2x-2\lambda y-8=0$. This family passes through two fixed points $A$ and $B$. Find the distance between these two points.