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 $2x - 3y + 3 = 0$ and $x + 2y + k = 0$ are conjugate lines with respect to the circle $S \equiv x^2 + y^2 + 8x - 6y - 24 = 0$,then the length of the tangent drawn from the point $\left(\frac{k}{4}, \frac{k}{3}\right)$ to the circle $S = 0$ is

From a point $(1,0)$ on the circle $x^2+y^2-2x+2y+1=0$,if chords are drawn to this circle,then the locus of the poles of these chords with respect to the circle $x^2+y^2=4$ is:

If $A(2, c)$ and $B(d, 2)$ are two points such that the polar of one point with respect to the circle $x^2+y^2=16$ passes through the other,then $c+d=$

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:

$A$ rectangle is formed by the lines $x=4, x=-2, y=5$,and $y=-2$. $A$ circle is drawn passing through the vertices of this rectangle. The pole of the line $y+2=0$ with respect to this circle is: