For $k > 0$, what is the area enclosed by the ellipse $\frac{x^{2}}{k^{2}} + \frac{y^{2}}{4k^{2}} = 1$?

Explanation

1. 01

   The semi-axes are $a = \sqrt{k^{2}} = k$ and $b = \sqrt{4k^{2}} = 2k$.

2. 02

   Area $= \pi ab = \pi \times k \times 2k = 2\pi k^{2}$ square units.