<p>The curve ${{C}_{1}}$ has equation ${{(y-a)}^{2}}-{{(kx+k)}^{2}}={{k}^{2}}$ where $a>1$ and $k>0$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">State a sequence of transformations which transforms the graph of ${{y}^{2}}-{{x}^{2}}=1$ to the graph of ${{C}_{1}}$.</span></div><p style="text-align: right;">[3]</p></li></ol>
<p><strong>For this question, your sketch should include the equations of any asymptotes and the coordinates of any turning points.</strong></p>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Given that ${{C}_{1}}$ intersects the $x$- axis at only one point, sketch the curve ${{C}_{1}}$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">On the same diagram, sketch the curve ${{C}_{2}}$ with equation</span></div><div class="list-item-paragraph" style="text-align: center">$y=\frac{1}{a+k\sqrt{1+{{\left( x+1 \right)}^{2}}}}$</div><p style="text-align: right;">[3]</p></li></ol></li></ol>

The curve ${{C}_{1}}$ has equation ${{(y-a)}^{2}}-{{(kx+k)}^{2}}={{k}^{2}}$ where $a>1$ and $k>0$.

State a sequence of transformations which transforms the graph of ${{y}^{2}}-{{x}^{2}}=1$ to the graph of ${{C}_{1}}$.

**For this question, your sketch should include the equations of any asymptotes and the coordinates of any turning points.**

Given that ${{C}_{1}}$ intersects the $x$- axis at only one point, sketch the curve ${{C}_{1}}$.

On the same diagram, sketch the curve ${{C}_{2}}$ with equation

Transformations of Graphs - General

Transformations of Graphs

International Baccalaureate Higher Level Mathematics

2020 NYJC CT2 P1 Q6

2020 NYJC CT2 P1 Q6

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