2021 ASRJC Promo Q4
A curve $C$ has equation
${{y}^{3}}-2x{{y}^{2}}+3{{x}^{2}}-3=0$
(i)
Find $\frac{\text{d}y}{\text{d}x}$ in terms of $x$ and $y$.
[2]
(ii)
Find the equation of the normal to the curve at the point $P\left( 2,3 \right)$.
[2]
(iii)
Given that $C$ meets the $y$-axis at the point $R$ and the normal in (ii) meets the $y$-axis at the point $A$, find the area of triangle $APR$ in the form $a-\sqrt[3]{b}$, where $a$ and $b$ are integers to be determined.
[3]
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