The equation of the pair of transverse common tangents drawn to the circles $x^2+y^2+2 x+2 y+1=0$ and $x^2+y^2-2 x-2 y+1=0$ is

If a circle passing through the point $(1,1)$ cuts the circles $x^2+y^2+4 x-5=0$ and $x^2+y^2-4 y+3=0$ orthogonally, then the centre of that circle is

Length of the common chord of the circles $x^2+y^2-6 x+5=0$ and $x^2+y^2+4 y-5=0$ is

The centroid of a variable $\triangle A B C$ is at the distance of 5 units from the origin. If $A=(2,3)$ and $B=(3,2)$, then the locus of $C$ is