RI/2021/JC1/Promo/P1/Q02

The curve $C$ has equation $y^3=4-\frac{x y^2}{2}$.
(i) Show that $\frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{y}{6 y+2 x}$.

[2]

(ii) Find the equation of the normal to $C$ at the point $P$ where $y=1$.

[3]