$x=a \sin (\omega t)$ 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 $=a c o t$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$I.$ Area $ABCD =$ Work done on the gas
$II.$ Area $ABCD =$ Net heat absorbed
$III.$ Change in the internal energy in cycle $= 0$
Which of these are correct