A)
Use Green's theorem to compute the area inside the ellipse $\displaystyle \frac{x^2}{5^2} + \frac{y^2}{12^2} = 1$.
Use the fact that the area can be written as
$$\iint_D dx\,dy = \frac12\int_{\partial D}-y\ dx + x\ dy \ .$$ Hint: $x(t) = 5 \cos(t)$.
The area is .

B)
Find a parametrization of the curve $x^{2/3} + y^{2/3} = 2^{2/3}$ and use it to compute the area of the interior.
Hint: $x(t) = 2 \cos^3(t)$.