<p>The curve $C$ has equation $\frac{9{{\left( y+3 \right)}^{2}}}{4}-\frac{{{\left( x-2 \right)}^{2}}}{4}=1$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Sketch $C$, stating the equations of any asymptotes and the coordinates of any turning points.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">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.<span class="inline-marks">[2]</span></div></li></ol>

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.

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.

2022 VJC Promo Q3

2022 VJC Promo Q3

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