<p>The parametric equations of a curve are</p>
<p style="text-align: center">$x=\sin t$, $y=\cos t$, where $0 < t < \frac{\pi }{2}$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Sketch the graph of the curve.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Show that the equation of the tangent to the curve at the point where $t=p$ is given by the equation $y=-\left( \tan p \right)x+\sec p$.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">Given that the above tangent meets the $x$-axis at the point $P$ and the $y$-axis at the point $Q$, find the coordinates of the mid-point $M$ of $PQ$ in terms of $p$.</div><div class="list-item-paragraph">Hence, determine the cartesian equation of the locus of $M$.</div><p style="text-align: right;">[3]</p></li></ol>

$x=\sin t$, $y=\cos t$, where $0 < t < \frac{\pi }{2}$.

Show that the equation of the tangent to the curve at the point where $t=p$ is given by the equation $y=-\left( \tan p \right)x+\sec p$.

Given that the above tangent meets the $x$-axis at the point $P$ and the $y$-axis at the point $Q$, find the coordinates of the mid-point $M$ of $PQ$ in terms of $p$.

Hence, determine the cartesian equation of the locus of $M$.

Parametric Equations

Graphing Techniques

H2 Math

International Baccalaureate Higher Level Mathematics

2019 RVHS P2 Q4

2019 RVHS P2 Q4

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