1. **Problem Statement:** Find the equation of a circle whose center is at the origin. 2. **Formula:** The general equation of a circle with center at $(h,k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. **Important Rule:** When the center is at the origin, $h=0$ and $k=0$, so the formula simplifies to: $$ x^2 + y^2 = r^2 $$ 4. **Explanation:** This means every point $(x,y)$ on the circle is at a distance $r$ from the origin. 5. **Final Equation:** Therefore, the equation of a circle centered at the origin with radius $r$ is: $$ x^2 + y^2 = r^2 $$ This equation represents all points $(x,y)$ that lie on the circle with radius $r$ centered at the origin.