What are the cuts of the graph by the planes of the system while solving from a multivariable calculus textbook I encountered this question: ''what are the cuts of the graph by the planes of the system?, explain this through $z =\sqrt{x^2 + y^2}$ and draw an adequate sketch''.
I can hardly comprehend the phrase ''what are the cuts of the graph by the planes of the system?'' which system? 
 A: Intersection with plane $z = {z_0}$:
$$\begin{gathered}
  \sqrt {{x^2} + {y^2}}  = {z_0} \hfill \\
  {x^2} + {y^2} = {\left( {{z_0}} \right)^2} \hfill \\
  x = {z_0}\cos (t) \hfill \\
  y = {z_0}\sin (t) \hfill \\ 
\end{gathered}$$
Intersecting curve:
$$c(t) = ({z_0}\cos (t),{z_0}\sin (t),{z_0})$$

Intersection with plane $y = {y_0}$:
$$\begin{gathered}
  \sqrt {{x^2} + {{\left( {{y_0}} \right)}^2}}  = z \hfill \\
  {x^2} + {\left( {{y_0}} \right)^2} = {z^2} \hfill \\
  {z^2} - {x^2} = {\left( {{y_0}} \right)^2} \hfill \\
  x = {y_0}\sinh (t) \hfill \\
  z = {y_0}\cosh (t) \hfill \\ 
\end{gathered}$$
Intersecting curve:
$$c(t) = ({y_0}\sinh (t),{y_0},{y_0}\cosh (t))$$

Intersection with plane $x = {x_0}$:
$$\begin{gathered}
  \sqrt {{{\left( {{x_0}} \right)}^2} + {y^2}}  = z \hfill \\
  {\left( {{x_0}} \right)^2} + {y^2} = {z^2} \hfill \\
  {z^2} - {y^2} = {\left( {{x_0}} \right)^2} \hfill \\
  y = {x_0}\sinh (t) \hfill \\
  z = {x_0}\cosh (t) \hfill \\ 
\end{gathered}$$
Intersecting curve:
$$c(t) = ({x_0},{x_0}\sinh (t),{x_0}\cosh (t))$$

