The polar of $(1, -2)$ with respect to $x^2+y^2-10x-10y+25=0$ is

The pole of the straight line $x+4y=4$ with respect to the ellipse $x^2+4y^2=4$ 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 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 coordinates of the pole of the line $lx + my + n = 0$ with respect to the circle $x^2 + y^2 = 1$ are: