Find Tangent to Ellipse: Dynamic Construction and Equation

This GeoGebra example demonstrates how to dynamically construct the tangent line to an ellipse at a given point and display its equation. The core mathematical concept is the tangent property of an ellipse in analytic geometry, where the tangent at a point (x0, y0) satisfies the equation xx0/a^2 + yy0/b^2 = 1. The construction uses a Textfield to input parameters a and b, defines the ellipse equation f, creates the Ellipse object, selects a point P on the ellipse, and uses the Line and EQtangent commands to generate the tangent line and its equation, with text objects text1 and text2 showing dynamic results. This is suitable for high school or early college students to explore the geometric and algebraic aspects of ellipse tangents, and for teachers to demonstrate how changing parameters affects the tangent line.