What is the radius of the circle represented by the equation x^2 + y^2 - 6x + 4y = 12?

General formula of the circle

(x-h) ² + (y-k) ² = r²

We are going to use formula a² + / -2ab + b² = (a-b) ² to complete the squares and to write the equation in the general form.

x² + y² - 6x + 4y = 12

x² - 6x + y² + 4y = 12

x² - 2*3x + 3² - 3² + y² + 2*2y + 2² - 2² = 12

(x-3) ² - 9 + (y+2) ² - 4 = 12

(x-3) ² + (y+2) ² = 12 + 13

(x-3) ² + (y+2) ² = 25

(x-3) ² + (y+2) ² = 5²

This circle has center (3,-2) and radius = 5.