Answer
$\displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{4}=1$
Work Step by Step
Square both parametric equations:
$\left\{\begin{array}{ll}
x^{2}=16\cos^{2}t & /\div 16\\
y^{2}=4\sin^{2}t & /\div 4
\end{array}\right.\qquad \Rightarrow\left\{\begin{array}{l}
\frac{x^{2}}{16}=\cos^{2}t \\
\frac{y^{2}}{4} = \sin^{2}t
\end{array}\right.$
Add the two equations$,\qquad\cos^{2}t +\sin^{2}t=1$
$\displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{4}=1\qquad$(an ellipse)
To graph, create a function value table using values for t, in ascending order of t, calculating the x- and y-coordinates of points on the graph.
Plot and join the points obtained with a smooth curve, noting the direction in which t increases.
