2022 DHS Promo Q5
A curve $C$ has equation $\frac{1-{{x}^{2}}{{y}^{2}}}{3{{y}^{2}}+{{x}^{2}}}=\frac{1}{2}$.
(a)
Show that $\frac{\text{d}y}{\text{d}x}=\frac{-x-2x{{y}^{2}}}{y\left( 3+2{{x}^{2}} \right)}$.
[3]
(b)
Find the equations of the tangents to the curve that are parallel to the $y$-axis.
[3]
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