Chapter 12.1, Problem 103E

To determine

To show:

The parameterization of the ellipse by the angle $\theta$ is $x=\frac{ab\cos \theta }{\sqrt{a^2{\sin }^2\theta +b^2{\cos }^2\theta }}$ and $y=\frac{ab\sin \theta }{\sqrt{a^2{\sin }^2\theta +b^2{\cos }^2\theta }}$.