How do you find the center and radius for x2+y212y+25=0?

1 Answer
Aug 1, 2016

Centre is thus (0,6) and radius is 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.

x2+y212y+25=0

Subtract 25 from both sides:

x2+y212y=25

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

x2+y212y+(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.

x2+(y6)2=11

This is now in the standard form

(xa)2+(yb)2=r2 for circle centre (a,b) and radius r.

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