Write the corresponding rectangular equation for the following parametric equation by eliminating $t$. Draw a graph of the plane curve using the rectangular equation. Indicate the direction of the curve that is obtained by using arrows that correspond to the increasing values of $t$.

$x=4\(\sin\) t,y=4\(\cos\) t$; $0\(\leq{t}\]\lt{2\pi}\)$

Write the corresponding rectangular equation for the following parametric equation by eliminating $t$. Draw a graph of the plane curve using the rectangular equation. Indicate the direction of the curve that is obtained by using arrows that correspond to the increasing values of $t$.

$x=4\(\csc\) t,y=2\(\cot\) t$

For a satellite moving in an elliptical path given by $x=-3+2\(\cos\) t$ and $y=4+5\(\sin\) t$, eliminate the parameter $t$ to express its path in the standard form of an ellipse.