Ellipse and String: Exploring the First Definition of Ellipse

This example demonstrates the classic definition of an ellipse—the locus of points where the sum of distances to two fixed foci remains constant. ①What it shows: Using a string (or stretchable line) to construct an ellipse, illustrating that any point on the ellipse maintains a constant sum of distances to the two foci. ②Core math concepts: First definition of ellipse, focal distance, ellipse equation, symmetry. ③Construction details (from GeoGebra commands): Ellipse command to draw the ellipse, Point command to create foci A, B and moving point P on the ellipse, button1/button2 to control point P's movement (button interaction), n as control parameter, f as related function. ④Target audience: Suitable for middle school to high school mathematics teaching, ideal for introductory analytic geometry lessons, ellipse property exploration, and mathematics competition training.