<p>A curve \(C\) has parametric equations \[x = t^2 + t, \quad y = t^2 - t, \quad t \in \mathbb{R}.\]</p>
<ol class="i-list"><li><div class="list-item-paragraph">Sketch the graph of \(C\), indicating the coordinates of the points where the curve crosses either axis.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find the coordinates of the point on \(C\) where the tangent to \(C\) is parallel to the line \(5y = 4x - 20\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the equation of the tangent to \(C\) at the point \((0,2)\) and show algebraically that this tangent does not cut \(C\) again.<span class="inline-marks">[5]</span></div></li></ol>

A curve \(C\) has parametric equations \[x = t^2 + t, \quad y = t^2 - t, \quad t \in \mathbb{R}.\]

Sketch the graph of \(C\), indicating the coordinates of the points where the curve crosses either axis.

Find the coordinates of the point on \(C\) where the tangent to \(C\) is parallel to the line \(5y = 4x - 20\).

Find the equation of the tangent to \(C\) at the point \((0,2)\) and show algebraically that this tangent does not cut \(C\) again.

2024 JPJC Promo Q10

2024 JPJC Promo Q10