If a diameter of the circle $x^2+y^2-4x+6y-12=0$ is a chord of a circle $S$ whose centre is at $(-3, 2)$,then the radius of $S$ is

From a point $P$ on the circle $x^2+y^2-4x-6y+9=0$,a pair of tangents $PQ$ and $PR$ are drawn touching the circle $x^2+y^2-4x-6y+12=0$ at $Q$ and $R$. If $C$ is the centre of the concentric circles,then the area of the $\triangle CQR$ (in sq. units) is

If $(\alpha, \beta)$ is the external centre of similitude of the circles $x^2+y^2=3$ and $x^2+y^2-2x+4y+4=0$,then $\frac{\beta}{\alpha}=$

The radius of the circle passing through the points of intersection of the circles $x^2+y^2+2x+4y+1=0$ and $x^2+y^2-2x-4y-4=0$ and intersecting the circle $x^2+y^2=6$ orthogonally is

If $S \equiv 2x^2+2y^2-8x+8y-7=0$ is the circle passing through the points of intersection of the circles $x^2+y^2+kx-ky+1=0$ and $x^2+y^2-kx+ky-2=0$,then the length of the tangent drawn from the point $(k, k)$ to the circle $S$ is

If $P$ is the point of contact of the circles $x^2+y^2+4x+4y-10=0$ and $x^2+y^2-6x-6y+10=0$,and $Q$ is their external centre of similitude,then the equation of the circle with $P$ and $Q$ as the extremities of its diameter is