<p>The curve $C$ has parametric equations</p>
<p style="text-align: center">$x={{t}^{2}}+4t$, $y={{t}^{3}}+{{t}^{2}}$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Sketch the curve for $-2\le t\le 1$.</span></div><p style="text-align: right;">[1]</p></li></ol>
<p>The tangent to the curve at point $P$ where $t=2$ is denoted by $l$.</p>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find the cartesian equation of $l$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">The tangent $l$ meets $C$ again at the point $Q$. Use a non-calculator method to find the coordinates of $Q$.</span></div><p style="text-align: right;">[4]</p></li></ol>

$x={{t}^{2}}+4t$, $y={{t}^{3}}+{{t}^{2}}$.

The tangent to the curve at point $P$ where $t=2$ is denoted by $l$.

The tangent $l$ meets $C$ again at the point $Q$. Use a non-calculator method to find the coordinates of $Q$.

N2009 P2 Q1

N2009 P2 Q1

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