Rotating a line in 3D yields a hyperbola?

This example demonstrates the geometric shape formed by rotating a line in three-dimensional space, revealing the relationship between rotational motion and conic sections, specifically hyperbolas. Key mathematical concepts include 3D coordinate transformations, rotation matrices, and the definition and properties of hyperbolas. The construction utilizes GeoGebra commands such as Line, Rotate, Intersect, and Segment, along with objects like a, A, B, b, α, b', D, c, d, e, E, F, G, f, C. It is suitable for high school and advanced students studying spatial geometry, analytical geometry, and parametric equations, helping them understand the formation of rotational solids and the generation mechanisms of conic sections.