<p>The curve \(C\) has equation \(y = \frac{x^2 - bx + b}{x - a}\), where&nbsp;\(a\) and \(b\) are constants. \(C\) has a vertical asymptote at \(x = 1\) and a turning point at \((0, -2)\).</p>
<ol class="i-list"><li><div class="list-item-paragraph">Determine the values of \(a\) and \(b\).<span class="inline-marks">[2]</span></div></li></ol>
<p>Use the values of \(a\) and \(b\) found in part <strong>(i)</strong> for the following parts.</p>
<ol class="i-list" start="3"><li><div class="list-item-paragraph">Sketch \(C\), stating the coordinates of any points of intersection with the axes and of any turning points and the equations of the asymptotes.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">By adding a suitable curve to your diagram in part <strong>(ii)</strong>, solve the inequality</div><div class="list-item-paragraph" style="text-align: center">\[\frac{x^2 - bx + b}{x - a} - \ln(5 - x) \ge 2.\]<span class="inline-marks">[3]</span></div></li></ol>

The curve \(C\) has equation \(y = \frac{x^2 - bx + b}{x - a}\), where \(a\) and \(b\) are constants. \(C\) has a vertical asymptote at \(x = 1\) and a turning point at \((0, -2)\).

Use the values of \(a\) and \(b\) found in part **(i)** for the following parts.

Sketch \(C\), stating the coordinates of any points of intersection with the axes and of any turning points and the equations of the asymptotes.

By adding a suitable curve to your diagram in part **(ii)**, solve the inequality

\[\frac{x^2 - bx + b}{x - a} - \ln(5 - x) \ge 2.\]

2024 MI PRU1 Q6

2024 MI PRU1 Q6