The equation of the bisector of the acute angle between the lines `2x-y+4=0` and `x-2y=1` is `x-y+5=0` `x-y+1=0` `x-y=5` (d) none of these

Options

A. `x + y+ 5=0`
B. `x-y+ 1=0`
C. ` x- y - 5=0`
D. none of these

Answer

B

Explanation

The equations of the lines are
`2x - y + 5 =0`
We have , `2x -1+(-1) xx 2 le 0 ` i.e, `a_(1)a_(2) +b_(1)b_(2) lt 0`
Therefore, the equation of the bisector of acute angle is
`(2x-y+4)/(sqrt(1+4)) = (-x+2y+1)/(sqrt((-1)^(2)+2^(2)))`
`rArr 2x - y + 4 = - x + 2y + 1`
`rArr 3x -3y + 3 = 0 rArr x -y + 1 =0`