The curve ${{C}_{1}}$ has equation ${{x}^{2}}-2x-4{{y}^{2}}=0$. Sketch the graph of ${{C}_{1}}$, sta

Question

The curve ${{C}_{1}}$ has equation ${{x}^{2}}-2x-4{{y}^{2}}=0$. Sketch the graph of ${{C}_{1}}$, stating clearly the coordinates of any points of intersection with the axes and the equations of any asymptotes. [3] By drawing a suitable graph ${{C}_{2}}$ on the same diagram, showing clearly the relative position with curve ${{C}_{1}}$, deduce the range of values of $k$ such that the equation ${{x}^{2}}-2x-4+\frac{4{{\left( x-2 \right)}^{2}}}{{{k}^{2}}}=0$ include non-positive root(s). [3]

Accepted Answer

(b)(i) Centre $(1, 0)$, Asymptotes: $y = \frac{x-1}{2}$ \text{ or } $y = -\frac{x-1}{2}$ (ii) $k \geq 2$

2022 TJC J1 MYE Q11

2022 TJC J1 MYE Q11

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