Calculus (3rd Edition)

The equation $$x^2+ \left(\frac{y}{4}\right)^{2} +z^2=1$$ is an ellipsoid. (See equations on page 691.) To find the trace with the plane $z=1/4$, we have $$x^2+ \left(\frac{y}{4}\right)^{2} +1/16=1\Longrightarrow x^2+ \left(\frac{y}{4}\right)^{2} =15/16$$ which is an ellipse in the $xy$-plane.