Question

Find the separate equation of the lines represented by the following equation.
$3x^2-2\sqrt{3}xy-3y^2=0$.

Answer 1

$3x^2-2\sqrt{3}xy-3y^2=0$.
$\therefore 3x^2-\sqrt{3}xy+\sqrt{3}xy-3y^2=0$
$\therefore 3x(x-\sqrt{3}y)+\sqrt{3}y(x-\sqrt{3}y)=0$
$\therefore (x-\sqrt{3}y)(3x+\sqrt{3}y)=0$
The separate equations of the lines are
$x-\sqrt{3}y=0$ and $3x+\sqrt{3}y=0$