Hyperbola with Vertical Axis: Investigating via Cone and Quadrilateral Construct

This GeoGebra example demonstrates the construction of a hyperbola with a vertical axis as a conic section, using a cone and a cutting plane, while incorporating a quadrilateral and its circumcircle to explore geometric relationships. The core mathematical concepts include the definition of a hyperbola (foci, transverse and conjugate axes), conic section generation, and properties of cyclic quadrilaterals. The construction employs GeoGebra commands such as Point, Segment, and Intersect, with objects including cone c, section curve f, quadrilateral ABCD, circumcircle c_1, foci F1 and F2, and a moving point P whose locus traces the hyperbola. This resource is suitable for high school or early college students studying conic sections, offering a dynamic bridge between 3D geometric intuition and 2D analytic equations, and can be used for guided inquiry in geometry or precalculus courses.