If $2 x-3 y+1=0$ is the equation of the polar of a point $P\left(x_1, y_1\right)$ with respect to the circle $x^2+y^2-2 x+4 y+3=0$, then $3 x_1-y_1=$

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