Answer
$ \displaystyle \frac{y^{2}}{25}+\frac{x^{2}}{16}=1$
Work Step by Step
From the parametric equations, we see that $x\in[-4,4], y\in[-5,5].$
Square both parametric equations:
$\left\{\begin{array}{ll}
x^{2}=16\cos^{2}t & /\div 16\\
y^{2}=25\sin^{2}t & /\div 25
\end{array}\right.$
$\left\{\begin{array}{l}
\frac{x^{2}}{16}=\cos^{2}t \\
\frac{y^{2}}{25} = \sin^{2}t
\end{array}\right.$
Add the two equations:
$\fbox{$ \displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{25}=1 $} $
(an ellipse centered at the origin, with the main axis on the y-axis, semiaxes: a=5 and b=4)
To emphasize the main axis being on y, we write
$ \displaystyle \frac{y^{2}}{25}+\frac{x^{2}}{16}=1$
To graph, create a table using several values for t, and then calculate $(x(t), y(t)),$ plotting the points as you go. Join with a smooth curve, noting the direction in which $t$ increases.