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

Consider the circles $S_1: x^2+y^2+2x+8y-23=0$ and $S_2: x^2+y^2-4x+10y+19=0$. If the polars of the centre of one circle with respect to the other circle are $L_1$ and $L_2$,then $L_1$ and $L_2$ are

The polar of the origin $(0, 0)$ with respect to the circle ${x^2} + {y^2} + 2\lambda x + 2\mu y + c = 0$ touches the circle ${x^2} + {y^2} = {r^2}$,if

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

If the points $(2,3)$ and $(K,-2)$ are conjugate with respect to the circle $x^2+y^2-2x+4y-2=0$,then $K=$

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: