367. Determine the geometric figure represented by the system of equations

$$
\left\{\begin{array}{l}
x^{2}+y^{2}+z^{2}-4 x=0 \\
y=1
\end{array}\right.
$$
Solution. Solving the given system of equations, we obtain the curve $x^{2}+z^{2}-4 x+1=0$, i.e., the circle $(x-2)^{2}+z^{2}=$ $=3$, lying in the plane $y=1$, with radius $R=\sqrt{ } \overline{3}$ and centered at the point $(2 ; 1 ; 0)$.