ACJC/2021/JC1/Promo/P1/Q03

A curve $C$ has equation
$\frac{x^2-4 y^2}{x^2+x y^2+100}=\frac{1}{2}, x \in \mathbb{R}, x \neq-8$
Show that $\frac{d y}{d x}=\frac{2 x-y^2}{2 x y+16 y}$.

[2]

Hence, prove that curve $C$ does not have any stationary point.

[3]