Chapter 13 - Vector Geometry - 13.6 A Survey of Quadratic Surfaces - Exercises - Page 692: 14

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$.