Ellipse-cone and sphere intersection guided by opening angles and radius

This example demonstrates how changing the opening angle and radius parameters produces the intersection curve of an elliptical cone and a sphere (a characteristic space curve/curve of intersection). It centers on key ideas in solid analytic geometry: quadric surfaces (elliptic cone and sphere), intersection of 3D surfaces producing the intersection locus, and equation-based/parameter-driven construction to visualize how geometry changes continuously. Construction highlights from the provided GeoGebra summary: CurveCartesian and Surface are used to build the relevant Cartesian curve and the quadric surfaces; objects such as j, n, r, a, and b organize the geometric parameters (including cone/ellipse parameters and sphere radius), while commondenom and eq1 indicate that a common denominator and a derived equation are formed to obtain a drawable relation for the intersection. The result is well suited for students in upper secondary to early university levels, especially for teaching and exploring 3D geometry, conic sections via quadrics, and equation-to-visualization workflows in GeoGebra.