Question:
Let the equation of the pair of lines, $\mathrm{y}=\mathrm{px}$ and $y=q x$, can be written as $(y-p x)(y-q x)=0$. Then the equation of the pair of the angle bisectors of the lines $x^{2}-4 x y-5 y^{2}=0$ is:
Correct Option: , 3
Solution:
$\frac{x^{2}-y^{2}}{1-(-5)}=\frac{x y}{-2}$
$\frac{x^{2}-y^{2}}{6}=\frac{x y}{-2}$
$\Rightarrow x^{2}-y^{2}=-3 x y$
$\Rightarrow x^{2}+3 x y-y^{2}=0$