Cross Sections of a Cone: Exploring Conic Sections Dynamically

This GeoGebra example demonstrates how different planes cutting through a cone produce various cross-sectional shapes, including circles, ellipses, parabolas, and hyperbolas. It visually connects the classic conic sections to their three-dimensional geometric origins. Core mathematical concepts include solid geometry, plane-section intersections, and the definition of conic sections. The construction uses GeoGebra commands such as Point, Intersect, Circle, Cone, Segment, Plane, IntersectPath, Corner, and OrthogonalLine to build the cone, cutting plane, and intersection path. Users can manipulate the plane or use sliders to observe how the section changes continuously. This resource is ideal for high school or early college students learning about conic sections, as well as for teachers seeking an interactive visual aid for classroom demonstrations or student-led exploration.