Example 2 (to $3^{\circ}$). Determine the type of surface and make a drawing: a) $y^{2}=4 x ;$ b) $z=x^{2}$; c) $y^{2}+z^{2}=4$.
Solution. a) Since the variable $z$ is missing in the equation of the surface, this is a cylinder with generators parallel to the $O z$ axis and the directrix - a parabola (Fig. 4.30) with equations

$$
\left\{\begin{array}{l}
y^{2}=4 x \\
z=0
\end{array}\right.
$$

b) Since the variable $y$ is missing in the equation of the surface, this is a cylinder with generators parallel to the $O y$ axis and the directrix - a parabola (Fig. 4.31) with equations

$$
\left\{\begin{array}{l}
z=x^{2} \\
y=0
\end{array}\right.
$$

![](https://cdn.mathpix.com/cropped/2024_05_22_8f5be56c3f01f571fd60g-051.jpg?height=373&width=418&top_left_y=1531&top_left_x=131)

Fig. 4.30

![](https://cdn.mathpix.com/cropped/2024_05_22_8f5be56c3f01f571fd60g-051.jpg?height=343&width=454&top_left_y=1559&top_left_x=720)

Fig. 4.31 c) A cylinder with generators parallel to the $O x$ axis and the directrix - a circle of radius 2 with equations (Fig. 4.32)

$$
\left\{\begin{array}{l}
y^{2}+z^{2}=4 \\
x=0
\end{array}\right.
$$