Geometric Definition of an Ellipse via Two Foci

This example illustrates the geometric definition of an ellipse: the locus of points in the plane whose sum of distances to two fixed foci remains constant. It emphasizes how the ellipse emerges from distance constraints and highlights the role of focus geometry, constant-sum property, and constructive geometry to turn a definition into a visible curve. Key concepts include ellipse, foci, distance-based loci, and geometric construction methods; auxiliary objects such as vectors and midpoints support the relationships used in the construction. Construction-wise, the applet uses commands such as Intersect, Ray, Point, Mirror, Line, Segment, Circle, and Ellipse to create the needed geometric elements; Distance is used to measure distances to the foci; If is used for conditional logic tied to the constant-sum requirement; OrthogonalLine and Mirror enable perpendicular and symmetric constructions; Vector and Midpoint help form supporting segments and reference points, while Polygon and text/trace objects provide visualization. Suitable for upper secondary students to early university learners studying coordinate/analytic geometry, loci, and classical geometric constructions.