How do you find the center and radius for x^2 + y^2 -12y + 25= 0?

1 Answer
Aug 1, 2016

Centre is thus (0,6) and radius is sqrt(11)

Explanation:

We want to complete the squares. As there is no x term of degree one we leave it as is and focus on the y.

x^2+y^2-12y+25=0

Subtract 25 from both sides:

x^2+y^2-12y = -25

Square half the coefficient of y and add to both sides:

x^2 + y^2 - 12y + (-6)^2 = -25 + (-6)^2

Recognise that because the constant term is half the coefficient we can convert the left hand side to squared form and simplify the right hand side.

x^2 + (y-6)^2 = 11

This is now in the standard form

(x-a)^2 + (y-b)^2 = r^2 for circle centre (a,b) and radius r.

Centre is thus (0,6) and radius is sqrt(11)