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

Question

The curve $C$ has equation $\frac{{{\left( y-2 \right)}^{2}}}{9}-\frac{{{\left( x-3 \right)}^{2}}}{4}=1$. Sketch $C$, giving the equations of its asymptotes and the coordinates of any turning points. [4] The curve $D$ has equation $12{{y}^{2}}-48y+48+a{{x}^{2}}-6ax-3a=0$, where $a$ is a positive constant. Find the set of values of $a$ for which $C$ and $D$ do not intersect. [2]

Accepted Answer

(i) Asymptotes: $y = 2 \pm \frac{3}{2}(x-3)$ (ii) $0 < a < 9$

2019 VJC Promo Q4

2019 VJC Promo Q4

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