Q:

Eliminate the parameter of a

Eliminate the parameter to find a description of the following circles
  or circular arcs in terms of $x$ and $y$. Give the center and radius,
  and indicate the positive orientation.
$x=4\cos{(t)} ,\ y=3\sin{(t)} ;\ 0 \leq t \leq 2\pi$

So,
$\displaystyle x^2=4^2\cos^2{(t)} ,\ y^2=3^2\sin^2{(t)} \implies \frac{x^2}{4^2}=\cos^2{(t)} ,\ \frac{y^2}{3^2}=\sin^2{(t)}$
But I detect no radius. I'm rather confused, on this whole question. It doesn't even explicitly define "the parameter". Insight?

A:

Those equations describe an ellipse, rather than a circle. I'm guessing that by radius they mean length of major and minor axes?
The parameter is $t$, and you're on the right track to eliminate it; your next step is to add the equations 
$$ \frac{x^2}{4^2}=\cos^2{(t)} \\ \frac{y^2}{3^2}=\sin^2{(t)}$$
and use the pythagorean identity.

