Pair of Straight Lines
3.0 Bisector of angle between the lines
3.0 Bisector of angle between the lines
The joint equation of bisectors of the angles between the lines represented by the equation $a{x^2} + 2hxy + b{y^2} = 0$ is $$\frac{{{x^2} - {y^2}}}{{a - b}} = \frac{{xy}}{h}$$
or, $$h{x^2} - (a - b)xy - h{y^2} = 0$$
i.e., coefficient of ${x^2}$ $+$ coefficient of ${y^2}$ $=0$.
Hence, the bisectors of the angle between the lines are always perpendicular to each other as shown in the figure.
