Question

Find the equation of the polar of $(1,-2)$ with respect to circle $x^2+y^2-10x-10y+25=0$.

Answer 1

Fact : Polar of point $(x_1,y_1)$ w.r.t. circle $S$ is given by $T=0$

So polar of $(1,-2)$ w.r.t. $x^2+y^2-10x-10y+25=0$ is given by,

$x\left(1\right)+y(-2)-5(x+1)-5(y-2)+25=0$

$\Rightarrow -4x-7y+30=0$

$\Rightarrow 4x+7y-30=0$