Determine the center and radius of the following circle equation:

x² + y² - 10x + 20y + 89 = 0

The center is (-5, - 10) and the radius = 6.

Step-by-step explanation:

Convert the equation to standard form by completing the square;

x^2 + y^2 - 10x + 20y + 89 = 0

x^2 + y^2 - 10x + 20y = - 89

x^2 - 10x + y^2 + 20y = - 89 Completing the square:

(x + 5) ^2 - 25 + (y + 10) ^2 - 100 = - 89

(x + 5) ^2 + (y + 10) ^2 = - 89 + 125

(x + 5) ^2 + (y + 10) ^2 = 36

Comparing this to the standard form:

(x - h) ^2 + (y - k) ^2 = r^2

- we see that the center is (-5, - 10) and the radius = 6.