Area of an elliptic? I'm looking for an analytic way to calculate the area of an elliptic described by $${x^2 \over a^2} + {y^2 \over b^2}=c^2$$
I saw it before, but now i've forgotten. I remember we set $x=a \cos x$ and $y=a \sin x$ but I don't remember what we did after that!

Certainly, if you are looking for a calculus approach, you can do it by assuming:
 $$x=ac\cos(t),~~y=bc\sin(t),~~~c\neq 0$$ in which $0\le t\le 2\pi$ (Here, I am assuming @David's comment) and then follow the integral: $$S=\frac{1}2\int_0^{2\pi}(xy'-yx')dt$$
Note that others may use $S=\int_0^{2\pi}xy' dt$ instead.
