Question

What loci are represented by the equation :
$x^3-x{y}^2=0.$

Answer 1

$x^3-x{y}^2=0x(x^2-y^2)=0x(x+y)(x-y)=0x=0,x=y,x=-y$

So the equation represents three straight lines one of which is the $y$ axis and the other two are the line $y=x$ and $y=-x$