9758/2021/P1/Q03

A curve has equation $x^{\frac{1}{2}}+y^{\frac{1}{2}}=3$, for $x>0$ and $y>0$.
(a) Show that $\frac{\mathrm{d} y}{\mathrm{~d} x}=-\left(\frac{y}{x}\right)^{\frac{1}{2}}$.

[2]

(b) Find the equation of the normal to the curve at the point where $x=1$.

[4]