Determine and state the coordinates of the center and the length of the radius of a circle whose equation is x² + y² - 6x = 56 - 8y

The center is at (3, - 4), and the radius is 9.

Step-by-step explanation:

x² + y² - 6x = 56 - 8y

Move x and y terms to one side.

x² - 6x + y² + 8y = 56

Complete the squares.

x² - 6x + 9 + y² + 8y + 16 = 56 + 9 + 16

(x - 3) ² + (y + 4) ² = 81

The center is at (3, - 4), and the radius is 9.