Bisectors of Angles between Two Straight Lines/General Form

Theorem
Let $\LL_1$ and $\LL_2$ be straight lines embedded in a cartesian plane $\CC$, expressed in general form as:

The angle bisectors of the angles formed at the point of intersection of $\LL_1$ and $\LL_2$ are given by:


 * $\dfrac {l_1 x + m_1 y + n_1} {\sqrt { {l_1}^2 + {m_1}^2} } = \pm \dfrac {l_2 x + m_2 y + n_2} {\sqrt { {l_2}^2 + {m_2}^2} }$

Proof
First we convert $\LL_1$ and $\LL_2$ into normal form:

Then from Bisectors of Angles between Two Straight Lines: Normal Form, the angle bisectors of the angles formed at the point of intersection of $\LL_1$ and $\LL_2$ are given by: