1. The problem asks to write the equation of a circle centered at the origin with radius 8. 2. The general formula for a circle centered at the origin is $$x^2 + y^2 = r^2$$ where $r$ is the radius. 3. Here, the radius $r = 8$, so substitute into the formula: $$x^2 + y^2 = 8^2$$ 4. Simplify the right side: $$x^2 + y^2 = 64$$ 5. This equation represents a circle centered at $(0,0)$ with radius 8, crossing the axes at $(8,0)$, $(-8,0)$, $(0,8)$, and $(0,-8)$ as given. Final answer: $$x^2 + y^2 = 64$$