X squared plus y squared - 12 y + 31 equals 0

x^2 + (y - 6) ^2 = 5 or x^2 + (y - 6) ^2 = (√5) ^2

Step-by-step explanation:

x^2 + y^2 - 12y + 31 = 0 can be rewritten in a form close to the equation of a circle centered at (h, k) and with radius r:

x^2 + y^2 - 12y + 31 = 0, or

(x - 0) ^2 + (y - 12y + 36) - 36 + 31 = 0, or

x^2 + (y - 6) ^2 = 5

Thus, x squared plus y squared - 12 y + 31 equals 0 actually represents the equation of a circle with center at (0, 6) and radius √5.