Elliptic Cone Intersection Construction

This GeoGebra example demonstrates the elliptic cone as a three-dimensional quadratic surface, focusing on constructing its intersection curve with a plane using the `IntersectPath` command. The construction employs objects `text1`, `text2`, `a`, `c`, `d` to define the intersecting entities, illustrating how GeoGebra computes and visualizes the locus of intersection points in 3D space. Core mathematical concepts include elliptic geometry, conic sections, three-dimensional analytic geometry, and surface intersections. The example is suitable for high school solid geometry and university multivariable calculus or analytic geometry courses, enabling students to explore the relationship between conical surfaces and planar cuts, and to dynamically adjust viewing angles or parameters for deeper insight into parametric representations and geometric transformations.