## Calculus (3rd Edition)

Ellipsoid; there is no trace with $y=5$.
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 $y=5$, we have $$x^2+ 25/16+z^2=1\Longrightarrow x^2+ z^2=-9/16$$ which is impossible and hence there is no trace with $y=5$.