The curve $C_1$ has equation $\frac{(x-1)^2}{16}-\frac{(y+3)^2}{4}=1$. Sketch $C_1$, giving th

Question

The curve $C_1$ has equation $\frac{(x-1)^2}{16}-\frac{(y+3)^2}{4}=1$. Sketch $C_1$, giving the equations of the asymptotes and the coordinates of the centre and vertices.[3] The curve $C_2$ has equation $x^2-4x+y^2+6y+13=a^2$, where $a>0$, intersects $C_1$ at exactly two points. Find the range of values of $a$.[3]

Accepted Answer

Centre $(1,-3)$, vertices $(-3,-3),(5,-3)$, asymptotes $y=\pm\dfrac12x+\cdots$; $3<a<5$

2025 VJC Promo Q2

2025 VJC Promo Q2

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