Final answer:
The equation of the circle with center (5, 1/4) and radius 6 is (x - 5)² + (y - 1/4)² = 36.
Step-by-step explanation:
To find the equation of a circle with a given center and radius, you can use the standard form of a circle's equation, which is (x - h)² + (y - k)² = r², where (h, k) are the coordinates of the center of the circle and r is the radius. The given center is (5, 1/4) and the radius is 6. Plugging these values into the standard form, we get:
(x - 5)² + (y - 1/4)² = 6².
Simplifying the radius squared, which is 36, we have the final equation of the circle:
(x - 5)² + (y - 1/4)² = 36.
This equation represents the circle on the coordinate plane with the specified center and radius.