Conic Sections via Plane–Cone Intersection

This example demonstrates how conic sections are formed when a plane intersects a cone at different orientations. By changing the relative position and angle of the intersecting plane, the construction reveals the resulting intersection curve (e.g., circle, ellipse, parabola, hyperbola) as a geometric object. The key math ideas are the definition of conics as the intersection of a plane with a conical surface and the way geometric parameters control the curve’s shape. Construction highlights include creating a 3D cone with InfiniteCone and a slicing Plane, then computing the intersection using Intersect/IntersectPath to obtain the conic curve. It also uses Vertex, Line, Ray, and Vector for reference geometry and directions; OrthogonalLine for perpendicular/auxiliary relationships; Circle and CircleArc for arcs in supporting constructions; Angle for measuring and displaying relevant angles; and Textfield for labeling parameters. Interactivity is driven by controls such as inputBox1/button1 and animation-related objects, with conditional logic (If) and optional symmetry (Mirror) to manage cases. Suitable for secondary to early university geometry instruction and interactive learning.