The curve $C$ has equation ${{a}^{2}}{{x}^{2}}-{{y}^{2}}-2\left( ax-2y+2 \right)=0$ where \

Question

The curve $C$ has equation ${{a}^{2}}{{x}^{2}}-{{y}^{2}}-2\left( ax-2y+2 \right)=0$ where $a$ is a constant such $a\in \mathbb{R}\backslash \left\{ 0 \right\}$. Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{a\left( ax-1 \right)}{y-2}$. Hence, find the coordinates of the points on $C$ at which the tangent is parallel to $y$-axis.[6]

Accepted Answer

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{a(ax-1)}{y-2}$. The tangents parallel to the $y$-axis occur at $(0,2)$ and $\left(\dfrac2a,2\right)$.

2019 EJC Promo Q3

2019 EJC Promo Q3

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