The curve $C_1$ has equation $$(x+3)^2-4(y+1)^2=16.$$ Sketch the curve $C_1$, stating the equati

Question

The curve $C_1$ has equation $$(x+3)^2-4(y+1)^2=16.$$ Sketch the curve $C_1$, stating the equations of any asymptote(s) and other key features clearly. [3] Another curve $C_2$ has parametric equations $x=t-\dfrac{1}{t-2}$ and $y=-t+5$ where $-2\leq t<2$. Find the coordinates of any point(s) of intersection between $C_1$ and $C_2$. [2] Sketch the curve $C_2$ on the same diagram as part (a), showing clearly any asymptote(s) and the coordinates of any axial intercept(s). [4]

Accepted Answer

(a) centre $(-3,-1)$, vertices $(-7,-1)$, $(1,-1)$, asymptotes $y=\dfrac{x}{2}+\dfrac12$, $y=-\dfrac{x}{2}-\dfrac52$ (b) $(6.34,3.22)$ (c) endpoint $(-\dfrac74,7)$, $y$-intercept $(0,5.41)$, asymptote $y=3$

2025 EJC Promo Q9

2025 EJC Promo Q9

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