1. The problem is to describe the graph of a circle centered at the origin $(0,0)$ with radius $1$. 2. The formula for a circle centered at $(h,k)$ with radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. Since the center is at $(0,0)$ and radius is $1$, the equation simplifies to: $$ x^2 + y^2 = 1^2 $$ $$ x^2 + y^2 = 1 $$ 4. This equation represents all points $(x,y)$ that are exactly $1$ unit away from the origin. 5. The graph is a perfect circle with radius $1$ centered at the origin. Final answer: The equation of the circle is $$ x^2 + y^2 = 1 $$.