Conic Sections using Perpendicular Bisectors

This GeoGebra example dynamically demonstrates the construction of conic sections (ellipse, hyperbola, parabola) using the property of perpendicular bisectors. The core mathematical concept is the definition of conics as loci of points where the sum or difference of distances to two foci is constant, and the perpendicular bisector as the locus of points equidistant from two points. The construction uses GeoGebra commands such as Circle, Point, and Sequence, involving objects F, E, d, O, B, c, C, D, a, and list1. By generating a series of perpendicular bisectors and tracing their intersections or envelopes, the conic curves emerge visually. This is suitable for high school students learning analytic geometry or conic definitions, and for teachers as an interactive classroom demonstration to illustrate the geometric essence and construction methods of conics.