Geometric Construction and Dynamic Demonstration of Ellipse Locus

This applet demonstrates the geometric construction of an ellipse locus in conic sections. Using GeoGebra commands such as Distance, Circle, Intersect, and Segment, it dynamically illustrates the formation mechanism of the locus of points on an ellipse. It is suitable for teaching and learning conic sections in high school mathematics, helping students intuitively understand the definition and geometric properties of ellipses. The construction is based on the fundamental definition of an ellipse: the set of all points whose sum of distances from two fixed foci is constant. In the applet, two fixed points serve as the foci, and circles centered at each focus with radii that maintain a constant sum are drawn. Their intersections trace out the elliptical curve. Students can interact with sliders and draggable points to modify key parameters, observing in real time how changes affect the shape, size, and eccentricity of the ellipse. This hands-on exploration reinforces the connection between the algebraic definition of an ellipse and its visual geometric representation. The applet also highlights the role of major and minor axes, the relationship between focal distance and eccentricity, and how the ellipse emerges naturally from the intersection of geometric loci. By making the abstract concept of a conic section tangible and dynamic, this tool supports conceptual understanding beyond rote memorization of formulas. It is designed for use in secondary education mathematics courses covering analytic geometry and conic sections, and can be effectively integrated into both classroom instruction and independent study. The interactive nature of the applet encourages inquiry-based learning, allowing students to formulate conjectures and verify them through direct manipulation.