Question

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

Answer 1

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

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.