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.
