Question

The equation of the bisector of the angle between the lines $2x+y-6=0$ and $2x-4y+7=0$ which contains the point $(1,2)$, is

• A. $6x-2y-5=0$
• B. $2x+6y-19=0$
• C. $6x+2y-5=0$
• D. $2x+6y+19=0$

Answer 1

The correct option is A $6x-2y-5=0$

Given lines are $l_1:2x+y-6=0$ and $l_2:2x-4y+7=0$
Rewritting the equation of lines,
$l_1:-2x-y+6=0,l_2:2x-4y+7=0$
Let $P=(1,2)$
$l_1\left(P\right)\cdot l_2\left(P\right)=2\times 1>0$
The angle bisector containing the point $(1,2)$ is given by
$\frac{-2x-y+6}{\sqrt{(-2{)}^2+(-1{)}^2}}=+\frac{2x-4y+7}{\sqrt{2^2+(-4{)}^2}}\Rightarrow 2(-2x-y+6)=2x-4y+7\therefore 6x-2y-5=0$