question_answer

The equation of the bisector of the acute angle between the lines \[2x-y+4=0\] and \[x-2y=1\] is

A)  \[x+y+5=0\]

B)         \[x-y+1=0\]

C)  \[x-y=5\]

D)  None of these

Correct Answer: B

Solution :

Clearly, from the figure, the origin is contained in the angle. Writing the equations of the lines as \[2x-y+4=0\] and \[-x+2y+1=0,\]the required bisector is

\[\frac{2x-y+4}{\sqrt{5}}=\frac{-x+2y+1}{\sqrt{5}}\]

\[2x-y+4=-x+2y+1\]

\[2x+x-y-2y+4-1=0\]

\[3x-3y+3=0\]\[\Rightarrow \]\[x-y+1=0\]