Question

The equations of bisectors of two lines $L_1 \& L_2$ are $2 x-16 y-5=0$ and $64 x+8 y+35=0$. If the line $L_1$ passes through $(-11,4)$, the equation of acute angle bisector of $L_1 \& L_2$ is :

• A. $2 x-16 y-5=0$
• B. $64 x+8 y+35=0$
• C. data insufficient
• D. none of these

Answer 1

Answer: (A)

$p=\left|\frac{-22-64-5}{\sqrt{2^2+(-16)^2}}\right|=\frac{91}{\sqrt{260}}$
$q=\left|\frac{-64 \times 11+8 \times 4+35}{\sqrt{64^2+8^2}}\right|=\frac{637}{2 \sqrt{260}}$
$p < q$ Hence $2 x-16 y-5=0$ is acute angle bisector