Derivation of the Sphere's Standard Equation

This example provides a visual tool to derive the standard form equation of a sphere. It demonstrates the geometric definition of a sphere (set of points equidistant from a center) and its algebraic transformation into (x−h)²+(y−k)²+(z−l）² = r². The GeoGebra construction uses commands such as Intersect, Point, Sphere, Plane, PointIn, OrthogonalLine, Line, Polygon, Segment, and Angle, and defines objects like O, B₁, a, C, b, P, etc., allowing dynamic manipulation of parameters a, b, c to illustrate the locus of the center and radius changes, leading to the final equation. It is intended for high‑school or early university students studying coordinate geometry and algebraic derivations.