A curve $C$ has equation $\frac{{{x}^{3}}-2{{y}^{2}}}{{{x}^{2}}+3xy}=1$. The points $P$ and \(

Question

A curve $C$ has equation $\frac{{{x}^{3}}-2{{y}^{2}}}{{{x}^{2}}+3xy}=1$. The points $P$ and $Q$ on $C$ each have $x$-coordinate $1$. Find the exact gradients of the tangents to $C$ at the points $P$ and $Q$.[5] Find the acute angle between the tangents to $C$ at the points $P$ and $Q$.[2]

Accepted Answer

(i) $-\frac{11}{6}$(ii) ${{79.8}^{\circ }}$(to 1d.p.) (or $1.39$ rad)

2021 ACJC P1 Q2

2021 ACJC P1 Q2

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