The pole of the straight line $x+4y=4$ with respect to the ellipse $x^2+4y^2=4$ is

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 $\sum_{i=1}^3 \frac{\alpha_i+\beta_i}{g_i}=$

The lines $x \cos \alpha + y \sin \alpha = P, \alpha \in R$ are chords of the hyperbola $\frac{x^2}{9} - \frac{y^2}{36} = 1$ and they subtend a right angle at the centre of the hyperbola. The locus of the poles of these lines with respect to the given hyperbola is

If $A(2, c)$ and $B(d, 2)$ are two points such that the polar of one point with respect to the circle $x^2+y^2=16$ passes through the other,then $c+d=$

If $2x - 3y + 1 = 0$ is the equation of the polar of a point $P(x_1, y_1)$ with respect to the circle $x^2 + y^2 - 2x + 4y + 3 = 0$,then $3x_1 - y_1 =$

If the inverse point of $(1,1)$ with respect to the circle $x^2+y^2-4x-6y+12=0$ is $(h, k)$,then $h+k$ is equal to