Final answer:
The equation of a circle centered at the origin with a radius of 12 is x² + y² = 144. This follows the standard circle equation (x - h)² + (y - k)² = r², simplifying to x² + y² = 12² since the circle's center is at (0, 0).
Step-by-step explanation:
The equation of a circle centered at the origin with a given radius can be found using the standard formula for a circle: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
Since the circle is centered at the origin, (h, k) is (0, 0), and the radius is given as 12.
Therefore, the equation simplifies to:
x² + y² = 12²
which further simplifies to:
x² + y² = 144
This equation represents a circle with a radius of 12 units centered at the origin (0,0) on a coordinate plane.