The equation of the polar of $(1, 1)$ with respect to the circle $x^2+y^2+4x+6y-3=0$ is

For all real values of $k$,the polar of the point $(2k, k-4)$ with respect to the circle $x^2+y^2-4x-6y+1=0$ passes through the point:

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

If $(4,2)$ and $(k,-3)$ are conjugate points with respect to $x^2+y^2-5x+8y+6=0$,then $k$ equals

The pole of the straight line $9x + y - 28 = 0$ with respect to the circle $2x^2 + 2y^2 - 3x + 5y - 7 = 0$ is

Consider the point $P(\alpha, \beta)$ on the line $2x+y=1$. If $P$ and $(3,2)$ are conjugate points with respect to the circle $x^2+y^2=4$,then $\alpha+\beta=$