Question

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. $x+y=5$

Answer 1

Answer: (B)

$x+y+1=0$

The angle of bisector of $2x+y+4=0$ and $x+2y=1$ is
$\frac{2x+y+4}{\sqrt{4+1+16}}=\pm \frac{x+2y-1}{\sqrt{1+4+1}}\Rightarrow \frac{2x+y+4}{\sqrt{21}}=\pm \frac{x+2y+1}{\sqrt{6}}$
Now for $2x+y+4=0$ and $-x-2y+1=0$
$a_1{a}_2+b_1{b}_2=2\times (-1)+1\times (-2)<0$
Therefore equation of angle bisector of acute angle is with negative sign
$\frac{2x+y+4}{\sqrt{21}}=-\frac{x+2y+1}{\sqrt{6}}\Rightarrow x+y+1=0$