Question

Find the separate equation of the lines represented by the following equation:
$2x^2+2xy-y^2=0$

Answer 1

The factors of the equation $x^2+2xy-y^2=0$ by the discriminant method are,

$x=\frac{-2y\pm \sqrt{{\left(2y\right)}^2-4\left(-y^2\right)}}{2}$

$=\frac{-2y\pm 2\sqrt{2}y}{2}$

$=-y\pm \sqrt{2}y$

$x=-y\left(1+\sqrt{2}\right),x=y\left(\sqrt{2}-1\right)$

$x+\left(1+\sqrt{2}\right)y=0,x-\left(\sqrt{2}-1\right)y=0$

Therefore, the separate equations of lines are $x+\left(1+\sqrt{2}\right)y=0$ and $x-\left(\sqrt{2}-1\right)y=0$.