The polar of a point with respect to the circle $x^2+y^2-10x+12y-3=0$,which is neither a tangent nor a chord of contact,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

The polars drawn from $(-1, 2)$ to the circles $S_1 \equiv x^2 + y^2 + 6y + 7 = 0$ and $S_2 \equiv x^2 + y^2 + 6x + 1 = 0$ are:

The pole of the straight line $x + 2y = 1$ with respect to the circle $x^2 + y^2 = 5$ is

Let $S \equiv x^2+y^2-8x+10y+5=0$ be a circle. Let $P(1,1)$ and $Q(1,-1)$ be two points. Then the point of intersection of the polar of $P$ with respect to $S=0$ and the chord with $Q$ as mid-point to $S=0$ is

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 $k=$