A particle moves in $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1-\cos \omega t)$ where $a$ and $\omega$ are constants. The particle traces
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A particle moves in $x y$ plane according to the law
$x=a \sin (\omega t)$ and $y=a(1-\cos (\omega t))$ where $a$ and $\omega$ are constants.
$\Rightarrow \sin ^2(\omega t)=\frac{x^2}{a^2}$
$\Rightarrow \cos ^2(\omega t)=\left(1-\frac{y}{a}\right)^2$
$\Rightarrow \frac{x^2}{a^2}+\left(1-\frac{y}{a}\right)^2=1$
$\Rightarrow x^2+(y-a)^2=a^2$
The given equation is the equation of circle with centre $(0, a)$, the radius a also the angular velocity is $\omega$ so distance covered $=a c o t$
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