Answer
Ellipse
Work Step by Step
We are given the parametric equations:
$\begin{cases}
x=a\sin t\\
y=b\cos t
\end{cases}$
To eliminate $t$, use the identity:
$\sin^2 t+\cos^2 t=1$
$\left(\dfrac{x}{a}\right)^2+\left(\dfrac{y}{b}\right)^2=1$
$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$
Therefore the parametric equations describe an ELLIPSE.
For
$\begin{cases}
x=2\sin t\\
y=3\cos t
\end{cases}$
The equation of the ellipse is:
$\dfrac{x^2}{2^2}+\dfrac{y^2}{3^2}=1$
$\dfrac{x^2}{4}+\dfrac{y^2}{9}=1$
