ACCESS Hyperbola 1: Geometric Construction of Foci and Asymptotes

This example demonstrates the fundamental geometric construction and properties of a hyperbola. By specifying parameters such as center, vertices, and foci, it uses lines, perpendiculars, and circles to build the key elements of the hyperbola step by step. Core mathematical concepts include the definition of a hyperbola (constant difference of distances to two foci), transverse and conjugate axes, foci, asymptotes, and eccentricity. Construction highlights: from the summary, the GeoGebra commands used are Line, Intersect, OrthogonalLine, and Circle, involving objects h, k, a, b, c, A, d, B, C, e, f, g, i, j, D, p, E, F, which together form the geometric framework of the hyperbola. Suitable for high school or early college analytic geometry courses, this example helps students intuitively understand the relationship between the standard equation and geometric elements of a hyperbola, and can serve as a classroom demonstration or self-exploration material.