<ol class="abc-list" start="2"><li><div class="list-item-paragraph">The curve ${{C}_{1}}$ has equation ${{x}^{2}}-2x-4{{y}^{2}}=0$.</div><ol class="i-list"><li><div class="list-item-paragraph">Sketch the graph of ${{C}_{1}}$, stating clearly the coordinates of any points of intersection with the axes and the equations of any asymptotes.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">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).</div><p style="text-align: right;">[3]</p></li></ol></li></ol>

The curve ${{C}_{1}}$ has equation ${{x}^{2}}-2x-4{{y}^{2}}=0$.

Parametric Equations

Graphing Techniques

H2 Math

International Baccalaureate Higher Level Mathematics

2022 TJC J1 MYE Q11

2022 TJC J1 MYE Q11

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