The equation of a circle is commonly expressed in the standard form:
(x – h)² + (y – k)² = r²
In this formula:
- (h, k) represents the coordinates of the center of the circle.
- r is the radius of the circle.
For our specific case:
- The center of the circle is at the origin, which means (h, k) = (0, 0).
- The radius r is given as 16.
Now, substituting these values into the standard equation:
(x – 0)² + (y – 0)² = 16²
This simplifies to:
x² + y² = 256
Therefore, the equation of the circle with its center at the origin and a radius of 16 is x² + y² = 256.