Question

Find the equation of the lines bisecting the angles between the line $Ax+By+C=0$ and the line passing through the point $(h,k)$ and perpendicular to this line.

Answer 1

The two lines are $Ax+By+C=0$ and $B(x-h)-A(y-k)=0$ as it is perpendicular to the above and passes through $(h,k)$
Their bisectors are
$\frac{B(x-h)-A(y-k)}{\sqrt{B^2+A^2}}=\pm \frac{Ax+By+C}{\sqrt{A^2+B^2}}$
or $B(x-h)-A(y-k)=\pm (Ax+By+C)$