Geometric Construction of an Ellipse Using Two Circles

This interactive applet demonstrates the geometric definition of an ellipse by constructing it through a two-circle method. It visually illustrates the fundamental property that the sum of the distances from any point on the ellipse to its two foci is constant. The construction involves points, circles, circular arcs, line segments, perpendicular lines, and loci, carefully layered to reveal the underlying geometry step by step. Students can dynamically manipulate the positions and radii of the two circles, observing in real time how the ellipse emerges from their intersection points and associated geometric traces. As the parameters change, learners see that regardless of which point is selected on the curve, the total distance to the two foci remains unchanged, reinforcing the formal definition of an ellipse. The applet also highlights the perpendiculars and segment relationships that arise during the construction, helping students connect the algebraic definition with its geometric origins. This hands-on exploration bridges intuitive visual reasoning and rigorous mathematical understanding, making it an excellent teaching tool for lessons on conic sections, locus problems, and classical geometric construction techniques.