1. The problem asks to write the equation of a circle given its center and radius. 2. The general formula for a circle with center at $(h,k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. For the first circle, the center is at the origin $(0,0)$ and the radius is 5 units. 4. Substitute $h=0$, $k=0$, and $r=5$ into the formula: $$ (x - 0)^2 + (y - 0)^2 = 5^2 $$ $$ x^2 + y^2 = 25 $$ 5. For the second circle, the center is also at the origin $(0,0)$ and the radius is 8 units. 6. Substitute $h=0$, $k=0$, and $r=8$ into the formula: $$ (x - 0)^2 + (y - 0)^2 = 8^2 $$ $$ x^2 + y^2 = 64 $$ 7. Therefore, the equations of the circles are: - First circle: $x^2 + y^2 = 25$ - Second circle: $x^2 + y^2 = 64$