Question

The following two sets of parametric functions both represent the same ellipse, Explain the difference between the graphs

Answer 1

SOLUTION

$\begin{gathered} x=3cost \\ y=8sint \\ 0\leq t\leq2\pi \end{gathered}$$\begin{gathered} x=3cos4t \\ y=8sin4t \\ 0\leq t\leq\frac{2\pi}{4} \\ \Rightarrow0\leq t\leq\frac{\pi}{2} \end{gathered}$