Final answer:
The equation for a circle with center (3, -2) and a radius of 6 is (x - 3)² + (y + 2)² = 36.
Step-by-step explanation:
The equation for a circle with center (3, −2) and a radius of 6 can be found using the standard formula for a circle: (x - h)² + (y - k)² = r², where (h, k) are the coordinates of the center and r is the radius. Plugging in the given center and radius, we get:
(x - 3)² + (y + 2)² = 6²
Simplifying the right side of the equation:
(x - 3)² + (y + 2)² = 36
This equation represents the circle with the specified center and radius on the Cartesian plane.