Hyperbola Tangent and Its Geometric Construction

①This example demonstrates the dynamic generation of a tangent line at a point on a hyperbola, along with the geometric relationships among the tangent, normal, and auxiliary lines. ②Core mathematical concepts include the definition of a tangent to a hyperbola, the slope of the tangent and normal, and the determination of the tangent via differential equations or geometric construction. ③Construction highlights: from the construction summary, GeoGebra commands such as Point, Segment, Slope, OrthogonalLine, and Line are used, with objects D, c, C, h, m, m_2, d, i, m_1, p, a, f, g, and text1, text2 for labeling and displaying slope values. ④Suitable for high school or college analytic geometry courses, this example helps students intuitively grasp the properties of hyperbola tangents and can serve as an interactive teaching aid.