2017 IJC Promo Q8

Timothy Gan

2017 IJC Promo Q8

A curve $D$ has parametric equations

$x=1-\cos \theta $, $y=\theta +\sin \theta $, for $0\le \theta \le 2\pi $.


Sketch the graph of $D$, stating the coordinates of any points of intersection with the axes.



Find $\frac{\text{d}y}{\text{d}x}$ in terms of $\theta$ .



A point $P$ on $D$ has parameter $\theta =\frac{\pi }{2}$ . The tangent to $D$ at $P$ cuts the $y$-axis at point $A$ and the normal to $D$ at $P$ cuts the $x$-axis at point $B$. Find the exact area of triangle $ABP$.


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Published: 15th June 2023

Written by

Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.

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