If one of the diameters of the circle,given by the equation $x^2 + y^2 - 4x + 6y - 12 = 0$,is a chord of a circle $S$ whose center is at $(-3, 2)$,then the radius of $S$ is:

If $2 x^{2}+2 y^{2}+4 x+5 y+1=0$ and $3 x^{2}+3 y^{2}+6 x-7 y+3 k=0$ are orthogonal,then the value of $k$ is

The line $x+y+2=0$ intersects the circle $x^2+y^2+4x-4y-4=0$ at two points $A$ and $B$. Let $S \equiv x^2+y^2+2gx+2fy+c=0$ be a different circle passing through the points $A$ and $B$. If the distance of the centre of $S=0$ from $AB$ is $\sqrt{2}$,then $g+f+c=$

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

If $(a, b)$ is the common point for the circles $x^2+y^2-4x+4y-1=0$ and $x^2+y^2+2x-4y+1=0$,then $a^2+b^2=$

The equation of a circle,which passes through the centre of the circle $x^2+y^2+8x+10y-7=0$ and is concentric with the circle $2x^2+2y^2-8x-12y-9=0$,is