Find the loci represented by the equation $\;$ $x^2 y + xy = 0$
The given equation is $\;$ $x^2 y + xy = 0$
The given equation can be written as $\;$ $xy \left(x + 1\right) = 0$
$\implies$ $xy = 0$ $\;$ or $\;$ $x + 1 = 0$
i.e. $\;$ $x = 0$ $\;$ or $\;$ $y = 0$ $\;$ or $\;$ $x = -1$
Hence, the given equation represents the lines
$x = 0$ $\;$ or $\;$ $y = 0$ $\;$ and $\;$ $x = -1$