1. **Stating the problem:** We are given a circle centered at point S with the equation $$x^2 + y^2 = 64$$. 2. **Formula and explanation:** The general equation of a circle centered at the origin is $$x^2 + y^2 = r^2$$, where $$r$$ is the radius. 3. **Identify the radius:** From the equation, $$r^2 = 64$$, so $$r = \sqrt{64} = 8$$. 4. **Interpretation:** This means the circle has a radius of 8 units and is centered at the origin (0,0). 5. **Summary:** The circle includes all points $$ (x,y) $$ such that the distance from the origin is 8 units. Final answer: The circle centered at S has radius 8 and equation $$x^2 + y^2 = 64$$.