the question i have is: the points A(2, 5) and B(-4, 13) lie at opposite ends of a diameter of a circle with centre C

a) find the radius of the circle- i did this by finding the diameter which was 10 and halving it, so the radius is 5

b) (which is the one i had a problem with): find the equation of the circle in the form

i found that the centre was (-1, 9) like so

and

so the equation of the circle would be this:

the answer the book gave was

which would imply that you made the squared constant terms positive, but it thought you would make them negative ie

does the method i used only work for certain things?

thanks