Intersecting a Cone and a Sphere: Constructing the Locus Curve

This example constructs a 3D cone and a sphere, then computes their intersection positions to visualize the resulting space curve (intersection line/curve) and its global locus. It highlights core solid-geometry ideas: cone/sphere modeling, orthogonal slicing by planes, geometric intersection (finding intersection points/paths), and locus-based reasoning to represent the set of points satisfying the intersection constraints. In GeoGebra, the build relies on commands such as Intersect (intersection), Circle (circles), Point (points), Cone (cone), Sphere (sphere), OrthogonalPlane (orthogonal plane), IntersectPath (intersection of paths), and Locus (locus/trajectory). These objects—Cone, Sphere, and OrthogonalPlane—provide the geometric framework; intersections are computed with Intersect/IntersectPath and collected to generate the locus curve. Suitable for advanced secondary school geometry, geometry construction lessons, and pre-university/early college instruction on space geometry and visualization.