The curve $C$ has equation \(\frac{9{{\left( y+3 \right)}^{2}}}{4}-\frac{{{\left( x-2 \right)}^{2}

Question

The curve $C$ has equation $\frac{9{{\left( y+3 \right)}^{2}}}{4}-\frac{{{\left( x-2 \right)}^{2}}}{4}=1$. Sketch $C$, stating the equations of any asymptotes and the coordinates of any turning points.[4] Hence find the set of values of $m$ such that the straight line with gradient $m$ that passes through the point $\left( 2,-3 \right)$ intersects $C$ at least once.[2]

Accepted Answer

(i) Asymptotes: $y = \frac{1}{3}x - \frac{11}{3}$ and $y = -\frac{1}{3}x - \frac{7}{3}$ (ii) $\left\{ m\in \mathbb{R}:m\frac{1}{3} \right\}$

2022 VJC Promo Q3

2022 VJC Promo Q3

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