Question

Find the equation of the bisector of the angle made by the $x-$ axis and $y-$ axis.

Answer 1

The equation of the coordinate axis are $x=0$ and $y0$ and intersect at the origin $(0,0)$.

The axis are perpendicular to each other and hence the angle between them is ${90}^o$.

So, the bisector of the angle between the coordinate axis will be ${45}^o$ and it will passes through the origin.

Thus, the required equation of bisector would be $y=\pm x$

using $y=mx$, $m=\tan \theta$

$\theta ={45}^o$.