3D Visualization of Parabola, Ellipse and Hyperbola as Conic Sections

① This example demonstrates how a plane intersecting an infinite cone generates the three classic conic sections: parabola, ellipse, and hyperbola, in a dynamic 3D environment. ② Core mathematical concepts include conic sections, the geometric definition of parabolas/ellipses/hyperbolas, plane-cone intersection, vectors and direction vectors, quadratic equations, and the Pythagorean theorem applied to spatial relationships. ③ Construction highlights: using GeoGebra commands such as InfiniteCone to create the cone, Line and Plane to define the cutting plane, IntersectPath to obtain the intersection curve, and Vector for directional vectors; additional objects include points A, B, C, D, E, lines f, g, h, planes α and β, and text labels text1–text4; derivative and definite integral commands may be used to explore curve properties. ④ Suitable for high school or early college courses in analytic geometry and calculus, this interactive visualization helps students grasp the unified origin of conic sections and serves as a powerful teaching aid or self-study tool.