Answer
$\displaystyle \frac{y^{2}}{25}+\frac{x^{2}}{16}=1$
Work Step by Step
Square both parametric equations:
$\left\{\begin{array}{ll}
x^{2}=16\cos^{2}t & /\div 16\\
y^{2}=25\sin^{2}t & /\div 25
\end{array}\right.\qquad \Rightarrow\left\{\begin{array}{l}
\frac{x^{2}}{16}=\cos^{2}t \\
\frac{y^{2}}{25} = \sin^{2}t
\end{array}\right.$
Add the two equations$,\qquad\cos^{2}t +\sin^{2}t=1$
$\displaystyle \frac{y^{2}}{25}+\frac{x^{2}}{16}=1$
(an ellipse centered at the origin, with the main axis on the y-axis).
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.
