Rolling Conic Sections: Dynamic Rolling of Ellipse, Parabola, and Hyperbola

This GeoGebra example demonstrates the dynamic rolling motion of conic sections (ellipse, parabola, hyperbola) along a line or another curve, showing how the focus or vertex traces a path during rolling. The core mathematical concepts involve tangent and normal lines to conics, focus-directrix properties, and the instantaneous center of rotation in rolling motion. Construction uses GeoGebra commands such as Point, OrthogonalLine, Intersect, Tangent, Circle, Line, and Parabola, with objects f, g, A, h, B, i, c, C, j, d, D, k, e, E, F, G, p, a, b, l, m, n. Sliders or animation controls allow users to vary rolling parameters and observe the locus of foci or vertices. Suitable for high school or college analytic geometry and geometric construction courses, this example provides an intuitive visualization of conic properties and rolling kinematics, ideal for mathematical experiments and inquiry-based learning.