Family of Circles

A circle cutting the circle $x^2+y^2=4$ orthogonally and having its centre on the line $2x-2y+9=0,$ passes through two fixed points. These points are

The equation of the circle which passes through the points of intersection of the circles $x^2+y^2-6x=0$ and $x^2+y^2-6y=0$ and has its centre at $\left(\frac{3}{2},\frac{3}{2}\right)$ is

If a circle $C$ passing through the point $(4,0)$ touches the circle $x^2+y^2+4x-6y=12$ externally at the point $(1,-1),$ then the radius of $C$ is

Equation of a circle having radius equal to twice the radius of the circle $x^2+y^2+\left(2p+3\right)x+\left(3-2p\right)y+p-3=0$ and touching it at the origin is