Locus of the Center of a Moving Circle as an Ellipse

This GeoGebra applet demonstrates the locus problem of the center of a moving circle. Given a fixed point A(1,0) and a fixed circle, a moving circle is constructed such that it passes through point A and is tangent to the fixed circle. Using geometric construction and the Locus command, the applet visualizes that the locus of the centers of all such moving circles forms an ellipse. This example integrates multiple geometric construction commands including points, circles, line segments, perpendicular bisectors, intersection points, and the Locus command, making it a classic dynamic demonstration of analytic geometry and the definitions of conic sections. Students can interactively drag the moving circle and observe how its center traces out an elliptical path in real time. The applet reinforces the fundamental definition of an ellipse as the set of points whose sum of distances to two fixed foci is constant, providing visual intuition that complements the algebraic treatment of ellipse equations. Educators can use this tool to guide inquiry-based learning, allowing students to explore the relationship between geometric construction and the analytical properties of ellipses, such as the positions of foci, the length of major and minor axes, and the standard form of the ellipse equation.