Now, since the purpose of this lab is not the algebra, I am accepting the formulas for circles. However, if you really want to calculate the ellipses area, there are numerous places that can help you.
My favorite site is called Egg curves. Note, however, that the equation that they give is for an ellipse in the center position, i.e., with center at (0,0).
Another interesting site is Math Forum Trig/Calc Problem of the week
And one with some java code!