Answer
$ \displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{4}=1$
Work Step by Step
From the parametric equations, we see that $x\in[-4,4], y\in[-2,2].$
Square both parametric equations:
$\left\{\begin{array}{ll}
x^{2}=16\cos^{2}t & /\div 16\\
y^{2}=4\sin^{2}t & /\div 4
\end{array}\right.$
$\left\{\begin{array}{l}
\frac{x^{2}}{16}=\cos^{2}t \\
\frac{y^{2}}{4} = \sin^{2}t
\end{array}\right.$
Add the two equations:
$\fbox{$ \displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{4}=1 $} $
(an ellipse centered at the origin with semiaxes a=4 and b=2)
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.
