Thomas' Calculus 13th Edition

There is no z in the equation; thus we have a cylinder. In the xy-plane (z=0), the trace is an ellipse $\displaystyle \frac{x^{2}}{(1/4)^{2}}+\frac{y^{2}}{(1/2)^{2}}=1$ and likewise in all the planes parallel to $z=0$. The resulting surface is an elliptical cylinder, with the z-axis as its axis.