Answer
$\begin{cases}
x=3\cos t\\
y=2\sin t
\end{cases}$
with $0\leq t\leq 2\pi$
Work Step by Step
The given curve is an ellipse centered at the origin with the elements:
$a=3$
$b=2$
The equation of the ellipse is:
$\dfrac{x^2}{3^2}+\dfrac{y^2}{2^2}=1$
$\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$
Find parametric equations that define an ellipse:
$\begin{cases}
x=a\cos t\\
y=b\sin t
\end{cases}$
with $0\leq t\leq 2\pi$
Substitute $a$ and $b$:
$\begin{cases}
x=3\cos t\\
y=2\sin t
\end{cases}$
with $0\leq t\leq 2\pi$
