Introduction to Conic Sections and Degenerate Conics

① This example demonstrates how a plane intersecting a cone in 3D space produces circles, ellipses, parabolas, hyperbolas, and degenerate conics (points or lines). ② Core mathematical concepts include the definition of conic sections, the geometry of plane-cone intersections, degenerate cases (plane passing through the vertex or parallel to a generator), and classification of intersection curves. ③ Construction highlights: using GeoGebra commands such as Point, Intersect, Cone, Plane, IntersectPath, and Corner, along with multiple points (A, B, C, D, etc.) and segments (a, b, c, etc.) to control the cone, cutting plane, and intersection path dynamically. ④ Suitable for high school or early college students as an introductory lesson on conic sections, and for teachers to visually explain the origin and degeneracy of these curves in a 3D context.