<p>A curve \(C\) has equation \(y = \frac{x^2 + 25x + 114}{x + 1}\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Sketch \(C\), indicating on the diagram the equations of any asymptotes, and the coordinates of any turning points and any axial intercepts.<span class="inline-marks">[4]</span></div></li></ol>
<p>A curve \(D\) has parametric equations</p>
<p style="text-align: center">\[x = 23\sin 2\theta - 1,\ y = 23 + 23\cos 2\theta\text{ for}\hspace{0.5em} -\frac{\pi}{2} &lt; \theta &lt; \frac{\pi}{2}.\]</p>
<ol class="abc-list" start="2"><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Find the cartesian equation of curve \(D\).<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Hence, on the same diagram as in part <strong>(a)</strong>, sketch the curve \(D\) and determine the number of intersection points between curve \(C\) and curve \(D\).<span class="inline-marks">[3]</span></div></li></ol>

A curve \(C\) has equation \(y = \frac{x^2 + 25x + 114}{x + 1}\).

Sketch \(C\), indicating on the diagram the equations of any asymptotes, and the coordinates of any turning points and any axial intercepts.

\[x = 23\sin 2\theta - 1,\ y = 23 + 23\cos 2\theta\text{ for } -\frac{\pi}{2} < \theta < \frac{\pi}{2}.\]

Find the cartesian equation of curve \(D\).

Hence, on the same diagram as in part **(a)**, sketch the curve \(D\) and determine the number of intersection points between curve \(C\) and curve \(D\).

2024 EJC P1 Q4

2024 EJC P1 Q4