8.0 Equation of angle bisector

8.1 Acute (internal) angle bisector and Obtuse (external) angle bisector

The equations of bisectors of angle between the lines $ax+by+c=0$ and $a'x+b'y+c'=0$ $(ab' \ne a'b)$ are given by $$\frac{{{a}x + {b}y + {c}}}{{\sqrt {{a}^2 + {b}^2} }} = \pm \frac{{a'x + b'y + c'}}{{\sqrt {a{'^2} + b{'^2}} }}$$