Question

The obtuse angle bisector between the lines $2x-y-4=0,x-2y+10=0$ is

• A. $x-y+7=0$
• B. $3x-y+5=0$
• C. $x+y-14=0$
• D. $2x+3y-5=0$

Answer 1

Answer: (C)

$x+y-14=0$

$2x-y-4=0$ and $x-2y+10=0$

Equation of angle bisector is

$\left|\frac{2x-y-4}{\sqrt{5}}\right|=\left|\frac{x-2y+10}{\sqrt{5}}\right|$

From +ve sign : $x+y-14=0$ or from -ve sign : $3x-3y+6=0$

This are two equation of angle bisector of given lines

So, we have to find obtuse angle bisector

$\therefore a_1{a}_2+b_1{b}_2=2\times 1+(-1)(-2)$

$=4>0$

$\therefore$ +ve sign gives obtuse angle bisector

$x+y-14=0$ is obtuse angle bisector.