Cross-sections of a Cylinder and a Cone (Hyperboloid): Constructing Intersection

This example demonstrates how to visualize the intersection or cross-section curves arising from a cylinder, a cone, and a hyperboloid-type surface. By varying a parameter, it shows how the resulting curves trace different shapes and how their geometric behavior can be studied. The key mathematics includes solid geometry cross-sections, analytic/coordinate geometry of conic-type intersection curves, parametric modeling, and continuity considerations. Construction-wise, it is built in GeoGebra using the command CurveCartesian to define Cartesian-coordinate curves; it relies on objects such as c_Z, zyl, c_K, hyppol, and the parameter t, together with several constructed curves (kurv_1, kurv_2, kurv_4, etc.) and reference points like P_1, P_2, kurv_3, and a to display the cross-section/intersection geometry clearly. Suitable for high-school to early undergraduate learners, especially for instruction and exploration of 3D analytic geometry and intersections of curved surfaces.