Hyperbola and Tangent Demonstration

This example shows a hyperbola together with the tangent line at a movable point on the curve. The key mathematical concepts are the standard equation of a hyperbola, the geometric definition of a tangent, the derivative as the slope of the tangent, and analytic geometry properties of conic sections. Construction uses GeoGebra commands Point (to create a dynamic point on the hyperbola), Tangent (to draw the tangent at that point), Intersect (to find intersections with axes or other objects), Polygon and Segment (to build auxiliary polygons and segments), and several text objects for labeling coordinates and formulas. It is suitable for high‑school conic sections lessons, university calculus courses illustrating the geometric meaning of derivatives, and as a resource for interactive geometry construction and dynamic visualization.