A particle is moving in $x-y$ plane whose $x$ and $y-$coordinates are $x=3\sin t2\pi t$ and $y=2\cos 2\pi t$, where $x$ and $y$ are in meter and $t$ is in second.

The correct option is A The path of the particle is elliptical
Given,
$x=3\sin 2\pi t$
$\Rightarrow \sin 2\pi t=\frac{x}{3}\dots \left(i\right)$
$y=2\cos 2\pi t$
$\Rightarrow \cos 2\pi t=\frac{y}{2}\dots \left(ii\right)$
Squaring and adding $\left(i\right)$ and $\left(ii\right)$,
${\sin }^{2}2\pi t+{\cos }^{2}2\pi t={\left(\frac{x}{3}\right)}^2+{\left(\frac{y}{2}\right)}^2$
$1=\frac{x^2}{9}+\frac{y^2}{4}$
It is an equation of ellipse.
Final Answer: (A)