Ellipses

I'm trying to find resources for ellipses (in particular, how to find the area of a section of an ellipse) and all I seem to find are websites that basically copied and pasted each other's information over and over again.

So do any of you /sci/fags know how to find the area of a section of an ellipse, either from one of the foci (like in Kepler's 2nd law of planetary motion) or from the center?

pi * (minor axis) * (major axis)