Answer
This surface is a cylinder.
Work Step by Step
\[
\begin{array}{l}
u \cos v=x \\
u^{2}=y \\
u \sin v=z
\end{array}
\]
Adding the squares of equations (1) and (3), we get:
\[
x^{2}+z^{2}=u^{2} \cos ^{2} v+u^{2} \sin ^{2} v=u^{2}\left(\cos ^{2} v+\sin ^{2} v\right)=u^{2}
\]
but $u^{2}=y,$ so
\[
x^{2}+z^{2}=y
\]
This surface is a cylinder.
