The equation of the polar of the point $(1, 2)$ with respect to the circle $x^2 + y^2 = 7$ is:

The locus of the poles of the tangents to the circle $x^2+y^2-2x+2y-2=0$ with respect to the circle $x^2+y^2=4$ is:

The point of concurrence of the polars of the variable point $(2t, t-4)$,where $t \in R$,with respect to the circle $x^2+y^2-4x-6y+1=0$ is

If the poles of the line $x-y=0$ with respect to the circles $x^2+y^2-2g_ix+c_i^2=0$ $(i=1, 2, 3)$ are $(\alpha_i, \beta_i)$,then $\sum_{i=1}^3 \frac{\alpha_i+\beta_i}{g_i}=$

The pole of the line $x-5y-7=0$ with respect to the circle $S \equiv x^2+y^2-2x+4y+1=0$ is $P(a, b)$. If $C$ is the centre of the circle $S=0$,then $PC=$

If $x+ky-4=0$ and $x+y-5=0$ are conjugate lines with respect to the circle $(x-1)^2+(y-1)^2=3$,then $k=$