Director Circle of a Hyperbola

This example demonstrates the geometric construction and properties of the orthoptic circle (director circle) of a hyperbola. The director circle is the locus of points where the angle bisectors of tangents to the hyperbola intersect. Key mathematical concepts involved include circle, hyperbola, 2D vectors, limits, and coordinate geometry. The construction uses GeoGebra commands such as Point, Tangent, and Angle to create points a, b, c, f, g, d, A, h, i, and angle α, illustrating the formation of the director circle. Suitable for high school and above mathematics learners to understand the geometric characteristics and applications of hyperbolas.