Dynamic Curve of Cone-Cylinder Intersection

① This example demonstrates the shape of the intersection curve between a cone and a cylinder in 3D space, and its dynamic evolution on a 2D projection as parameters change, showing transitions from ellipses to other curve types. ② Core mathematical concepts include surface equations of cones and cylinders, parametric representation of the intersection curve, and the use of derivatives to analyze tangent directions and rates of change, along with properties of ellipses and circumcircles. ③ Construction highlights: using GeoGebra commands such as Sequence to generate point sequences, Point to construct key points, and LaTeX to display formulas; key objects include parameters B, r, dz, dx, surface functions f1z_x and f2z_x, the intersection line l1, point lists list1yz and list2yz, and sliders to control parameters, ultimately plotting the intersection locus. ④ Suitable for high school to university level courses in solid geometry, analytic geometry, or calculus, serving as an interactive tool to visualize the generation and properties of surface intersection curves.