If a unit circle $S \equiv x^2+y^2+2 g x+2 f y+c=0$ touches the circle $S^{\prime} \equiv x^2+y^2-6 x+6 y+2=0$ externally at the point $(-1,-3)$, then $g+f+c=$

$3 x+4 y-43=0$ is a tangent to the circle $S \equiv x^2+y^2-6 x+8 y+k=0$ at a point $P$. If $C$ is the centre of the circle and $Q$ is a point which divides $C P$ in the ratio $-1: 2$, then the power of the point $Q$ with respect to the circle $S=0$ is

If the radical axis of the circles $x^2+y^2+2 g x+2 f y+c=0$ 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

After the coordinate axes are rotated through an angle $\frac{\pi}{4}$ in the anti-clockwise direction without shifting the origin, if the equation $x^2+y^2-2 x-4 y-20=0$ transforms to $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ in the new coordinate system, then

$$ \left|\begin{array}{lll} a & h & g \\ h & b & f \\ g & f & c \end{array}\right|= $$