If the equation of the polar of the point $(\alpha, -1)$ with respect to the circle $x^2+y^2-4x-6y-12=0$ is $y=\beta$,then $4(\alpha+\beta)=$

If the poles of the line $x-y=0$ with respect to the circles $x^2+y^2-2g_ix+c_i^2=0$ $(i=1, 2, 3)$ are $(\alpha_i, \beta_i)$,then $\sum_{i=1}^3 \frac{\alpha_i+\beta_i}{g_i}=$

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:

For all real values of $k$,the point which lies on the polar of $(k, k+1)$ with respect to the circle $x^2+y^2+4x-8y-5=0$ is

The pole of the line $x+y+2=0$ with respect to the circle $x^2+y^2-4x+6y-12=0$ 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: