The problem asks to identify which of the statements are correct. Let us analyze each statement carefully.

1. Однополостный гиперболоид является частным случаем цилиндрической поверхности.

   • This is incorrect. A one-sheet hyperboloid is not a special case of a cylindrical surface because a hyperboloid is not generated by parallel lines (a key feature of cylindrical surfaces). It is instead a ruled surface but distinctly different from cylindrical surfaces.

2. При вращении гиперболы вокруг действительной оси получается двуполостный гиперболоид.

   • This is correct. When a hyperbola rotates around its real (transverse) axis, it generates a two-sheet hyperboloid. This follows from the geometric definition of hyperboloids.

3. Цилиндрические поверхности являются частным случаем конической поверхности.

   • This is correct. A cylindrical surface can be viewed as a degenerate case of a conical surface where the vertex is moved infinitely far away. This means the generatrix remains parallel.

4. В сечениях эллиптического параболоида $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 2z$ плоскостями $z = z_0$ получается эллипс, минимый эллипс или точка, в сечениях плоскостями $y = y_0$ и $x = x_0$ получаются параболы.

   • This is correct. For an elliptic paraboloid, horizontal sections ($z = z_0$) yield ellipses (or degenerations like points for $z_0 = 0$), while vertical sections ($x = x_0$ or $y = y_0$) produce parabolas.

Correct Statements:

• 2, 3, and 4 are correct.

Would you like further clarification or a deeper explanation? Here are some additional questions related to this problem:

1. What are the main geometric differences between a hyperboloid and a cylindrical surface?
2. Why does the rotation of a hyperbola around its axes lead to one-sheet or two-sheet hyperboloids?
3. How does an elliptic paraboloid differ from a hyperbolic paraboloid in terms of sections?
4. Can you explain the role of degenerate cases (like points or lines) in surface intersections?
5. How is a cylindrical surface mathematically related to a cone?

Tip: Always visualize surfaces by plotting their cross-sections to better understand their properties!