<p>A curve $C$ has equation $y=\frac{{{x}^{2}}-4x+4}{x-1}$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Sketch $C$, stating clearly the equations of any asymptotes; coordinates of turning points and points of intersection with the axes.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">By drawing a suitable graph on the same diagram in part <strong>(a)</strong>, find the range of values of $b$, where&nbsp;$b&gt;0$, such that the equation ${{\left( x-2 \right)}^{2}}+\frac{1}{{{b}^{2}}}{{\left( \frac{{{x}^{2}}-4x+4}{x-1}+1 \right)}^{2}}=4$ has no real roots.<span class="inline-marks">[3]</span></div></li></ol>

A curve $C$ has equation $y=\frac{{{x}^{2}}-4x+4}{x-1}$.

Sketch $C$, stating clearly the equations of any asymptotes; coordinates of turning points and points of intersection with the axes.

By drawing a suitable graph on the same diagram in part **(a)**, find the range of values of $b$, where $b>0$, such that the equation ${{\left( x-2 \right)}^{2}}+\frac{1}{{{b}^{2}}}{{\left( \frac{{{x}^{2}}-4x+4}{x-1}+1 \right)}^{2}}=4$ has no real roots.

2024 CJC Promo Q4

2024 CJC Promo Q4

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