Use Green's theorem to compute the area inside the ellipse $\displaystyle \frac{x^2}{5^2} + \frac{y^2}{12^2} = 1$.
That is use the fact that the area can be written as
$$\iint_D dx\,dy = \iint_D (\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}) dx \,dy = \int_{\partial D}P dx + Qdy$$ for appropriately chosen $P$ and $Q$.
The area is .