Question

Find the polar of the point (-2,3) with respect to the circle $x^2+y^2-4x-6y+5=0.$

Answer 1

The polar of the general equation of circle w.r.t point $(x_1,y_1)$ is

$x{x}_1+y{y}_1+g(x+x_1)+f(y+y_1)+c=0$

Then, the polar of the general equation of given circle w.r.t point $(-2,3)$ is

$\Rightarrow x(-2)+y\left(3\right)-2(x-2)-3(y+3)+5=0$

$\Rightarrow -4x+0+4-9+5=0$

Equation of polar is $x=0$