The radical axis of the circle $x^2+y^2+2 g x+2 f y+c=0$ and $2 x^2+2 y^2+3 x+8 y+2 c=0$ touches the circle $x^2+y^2+2 x+2 y+1=0$. Then,

$2 x-3 y+1=0$ and $4 x-5 y-1=0$ are the equations of two diameters of the circle $S \equiv x^2+y^2+2 g x+2 f y-11=0 . Q$ and $R$ are the points of contact of the tangents drawn from the point $P(-2,-2)$ to this circle. If $C$ is the centre of the circle $S=0$, then the area (in square units ) of the quadrilateral $P Q C R$ is

If the inverse point of the point $(-1,1)$ with respect to the circle $x^2+y^2-2 x+2 y-1=0$ is $(p, q)$, then $p^2+q^2=$

If $(a, b)$ is the mid-point of the chord $2 x-y+3=0$ of the circle $x^2+y^2+6 x-4 y+4=0$, then $2 a+3 b=$