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!

[It is not clear to us what you mean by analytic, esp with the tags of geometry and algebra-precalc]
The approach I'd use, is to consider the unit circle, and think about how much you need to stretch it in the $x$ and $y$ direction, in order to get an ellipse.

 Starting from the unit circle $x^2 + y^2 = 1$, we need to stretch it by $\frac{a}{c} $ in the $x-$ direction and $\frac{b}{c} $ in the $y-$ direction, to get the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = c^2$.
 How does this change the area of the unit circle, which is $\pi1^2$?

