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

The equations of the tangents drawn from the origin to the circle $x^2+y^2+2 g x+2 f y+g^2=0$ are

If $2 x+y=0$ is the equation of a chord of the circle $x^2+y^2-2 x-6 y+3=0$, then the circle with this chord as diameter passes through the point

If the radical axis of the circles $x^2+y^2+2 \alpha x+2 \beta y+c=0$ and $x^2+y^2+\frac{3}{2} x+4 y+c=0$ touches the circle $x^2+y^2+2 x+2 y+1=0$, then $4 \alpha \beta-8 \alpha-3 \beta+10=$