The folium of Descartes is a curve given by the equation ${{x}^{3}}-9xy+{{y}^{3}}=0$. Find the equ

Question

The folium of Descartes is a curve given by the equation ${{x}^{3}}-9xy+{{y}^{3}}=0$. Find the equation of the tangent to the curve at the point $\left( 4,2 \right)$.[4] Find the exact coordinates of the point, other than the origin, where the tangent to the curve is parallel to the $y$-axis.[4]

Accepted Answer

(i) $y=\frac{5}{4}x-3$ (ii) $\left( 3\left( {{2}^{\frac{2}{3}}} \right),3\left( {{2}^{\frac{1}{3}}} \right) \right)$

2021 TMJC P1 Q6

2021 TMJC P1 Q6

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