Chapter 11.7, Problem 53ES

If a sphere $\frac{x^2}{a^2}+\frac{y^2}{a^2}+\frac{z^2}{a^2}=1$ of radius a is compressed in the z-direction, then the resulting surface, called an oblate spheroid, has an equation of the form $\frac{x^2}{a^2}+\frac{y^2}{a^2}+\frac{z^2}{c^2}=1$ where $c<a.$ Show that the oblate spheroid has a circular trace of radius a in the xy-plane and an elliptical trace in the xz-plane with major axis of length 2a along the x-axis and minor axis of length $2c$ along the z-axis.