A curve $C$ has equation $\frac{1-{{x}^{2}}{{y}^{2}}}{3{{y}^{2}}+{{x}^{2}}}=\frac{1}{2}$. Show t

Question

A curve $C$ has equation $\frac{1-{{x}^{2}}{{y}^{2}}}{3{{y}^{2}}+{{x}^{2}}}=\frac{1}{2}$. Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{-x-2x{{y}^{2}}}{y\left( 3+2{{x}^{2}} \right)}$.[3] Find the equations of the tangents to the curve that are parallel to the $y$-axis.[3]

Accepted Answer

(b) $x=\sqrt{2}$ and $x=-\sqrt{2}$

2022 DHS Promo Q5

2022 DHS Promo Q5

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