Understanding the Role of a, b, and r in the Circle Equation (x‑a)² + (y‑b)² = r

This example illustrates how the parameters a, b, and r determine the position and size of a circle given by the equation (x‑a)² + (y‑b)² = r². It demonstrates the concept of coordinate geometry, specifically the standard form of a circle's equation, and shows how the center (a,b) and radius r affect the graph. Using GeoGebra, the construction employs objects a, b, r as sliders, creates the circle c, draws tangents, orthogonal lines, intersections, and segments to visualize geometric relationships. The activity is suitable for middle‑school and high‑school students learning analytic geometry and for teachers preparing interactive lessons.