### 2022 DHS Promo Q5

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 $frac{text{d}y}{text{d}x}=frac{-x-2x{{y}^{2}}}{yleft( 3+2{{x}^{2}} right)}$. [3] (b) Find the equations of the tangents to the curve that are parallel