The line $x+y+1=0$ intersects the circle $x^{2}+y^{2}-4 x+2 y-4=0$ at the points $A$ and $B$. If $M(a, b)$ is the mid-point of $A B$, then $a-b=$

A circle $S$ passes through the points of intersection of the circles $x^{2}+y^{2}-2 x-3=0$ and $x^{2}+y^{2}-2 y=0$. If $x+y+1=0$ is a tangent to the circle $S$, then equation of $S$ is

If the common chord of the circles $x^{2}+y^{2}-2 x+2 y+1=0$ and $x^{2}+y^{2}-2 x-2 y-2=0$ is the diameter of a circle $S$, then the center of the circles is

A rhombus is inscribed in the region common to the two circles $x^{2}+y^{2}-4 x-12=0$ and $x^{2}+y^{2}+4 x-12=0$. If the line joining the centres of these circles and the common chord of them are the diagonals of this rhombus, then the area (in sq units) of the rhombus is