A curve $C$ has equation ${{\left( y-kx \right)}^{2}}+8y-12=0$, where $k$ is a real constant. Find $

Question

A curve $C$ has equation ${{\left( y-kx \right)}^{2}}+8y-12=0$, where $k$ is a real constant. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x,y$ and $k$. [2] The tangent to $C$ at the point where $x=2$ is parallel to the $y$-axis. Find the value of $k$. [3]

Accepted Answer

(i) $\frac{dy}{dx}= rac{k(y-kx)}{y-kx+4}$; (ii) $k= rac74$

2020 ACJC PROMO Q3

2020 ACJC PROMO Q3

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