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 condition for the lines $lx + my + n = 0$ and $l_1x + m_1y + n_1 = 0$ to be conjugate with respect to the circle $x^2 + y^2 = r^2$ is:

The normal to a circle $S=0$ at $P(1,3)$ is $x+2y=7$ and it has another normal at $Q(3,5)$ which is the polar of the point $A(7, -1/2)$ with respect to the circle $x^2+y^2-4x+6y-12=0$. Then,the equation of the circle $S=0$ is

The locus of the poles of normal chords of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is given by:

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: