Answer
The surface is a sphere with a center $C(0,1 / 2,0)$ and a radius $r=1 / 2$
Work Step by Step
There is given a surface
\[
0=-y+z^{2}+y^{2}+x^{2}
\]
This surface is a sphere. We should complete squares to find its center and radius.
\[
\begin{aligned}
0=-y+z^{2}+x^{2}+y^{2} & \Rightarrow 0=z^{2}+x^{2}+\left(-y+y^{2}\right) \\
& \Rightarrow (1 / 2)^{2}=z^{2}+x^{2}+\left[-2(1 / 2) y+y^{2}+(1 / 2)^{2}\right] \\
& \Rightarrow (1 / 2)^{2}=(-1 / 2+y)^{2}+x^{2}+z^{2}
\end{aligned}
\]
And therefore, the surface is a sphere with a center $C(0,1 / 2,0)$ and a radius $r=1 / 2$
