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{\bf Question}
A wheel of radius $a$ and centre $C$ rolls along a horizontal
straight line without slipping. Find the parametric equation for
the locus of a fixed point $P$ on a spoke of the wheel at distance
b from its centre. Take the x axis as the line through a low
point of the curve and the parameter $t$ as the angle $PCA,$ where
$A$ is the point of contact of the wheel during the rolling.
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{\bf Answer}
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We know: the arc $QL = at$ so $OL = at$ and $PM=b\sin t$ and $CM =
b\cos t$
So the coordinates of P are \begin{eqnarray*} x & = & at - b\sin
t \\ y & = & a - b\cos t \end{eqnarray*}
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