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Q. The equation of the bisector of the acute angle between the lines $2 x-y+4=0$ and $x-2 y=1$ is

Straight Lines

Solution:

image
Clearly, from the figure, the origin is contained in the acute angle. Writing the equations of the lines as
$2 x-y+4=0$ and $-x+2 y+1=0$,
the required bisector is
$\frac{2 x-y+4}{\sqrt{5}}=\frac{-x+2 y+1}{\sqrt{5}}$