Formation of Ellipse: A Verification with Foci, Segments, and Interactive Contro

This GeoGebra example demonstrates the formation of an ellipse through an interactive verification of its defining property: the set of points where the sum of distances to two fixed foci is constant. It visually confirms the geometric definition of an ellipse, linking it to the algebraic quadratic equation and the roles of foci, major/minor axes. The construction uses the Focus command to place two foci F and F', a Point C moving in the plane, and Segment commands to connect C to each focus, measuring the sum of segment lengths. A slider t controls the constant sum, and a locus or parametric plot generates the ellipse curve. Buttons (button1, button3) allow verification and reset actions. This resource is suitable for high school analytic geometry or introductory college geometry, helping students grasp the essence of ellipse formation through dynamic manipulation and reinforcing the connection between geometric loci and algebraic representations.