Spatial Conic Sections via Cutting a Cone with Moving Planes

This GeoGebra example demonstrates how different 2D conic sections emerge as a plane intersects a cone in space. By moving and rotating the cutting plane, the intersection curve transforms, illustrating the geometric mechanism behind ellipses, parabolas, and hyperbolas. The key mathematics concepts include the definition of conic sections through cone–plane intersection, the role of plane position and orientation in determining the curve type, and supporting relations connected to linear functions, trigonometric/tangent-related geometry, and an integration perspective for interpreting curve-related accumulated quantities. Construction-wise, it leverages GeoGebra commands such as OrthogonalLine, Point, Midpoint, Line, Vector, Plane, Translate, Rotate, Sequence, and IntersectPath. The objects Plane/Planexy and Rotationplane (together with translateplanexy) manage the plane setup and its transformations, while opacity controls the visualization layers between the 3D cone/planes and the resulting intersection curve. Suitable for high-school to early university instruction in geometry and analytic geometry, with interactive value for conceptual understanding and guided exploration.