The equation of bisectors of the angle between the lines given by $3 x^2+5 x y+4 y^2=0$ is
The equation of bisectors of the angle between the lines given by $3 x^2+5 x y+4 y^2=0$ is
$x^2-y^2-\frac{2}{5} x y=0$
$x^2-y^2+\frac{2}{5} x y=0$
$x^2-y^2-\frac{1}{5} x y=0$
$x^2-y^2+\frac{1}{5} x y=0$
Solution
The equation of the bisectors of the angle between the line $3 x^2+5 x y+4 y^2=0$ is
$\frac{x^2-y^2}{3-4}=\frac{x y}{\frac{5}{2}}$
or $\quad x^2-y^2=-\frac{2}{5} x y$
i.e. $x^2-y^2+\frac{2}{5} x y=0$