Question

Find the center and the radius of the following circles:
(a) x^2 +y^2 −6x+y=3
(b)x^2 +y^2 +8x=0
(c)x^2 +y^2 +2x−8y=−8

Answer 1

I'll do (c) and the others work the same way. You just complete the squares:

x^2 +y^2 +2x−8y = −8
x^2+2x + y^2-8y = -8
x^2+2x+1 + y^2-8y+16 = -8+1+16
(x+1)^2 + (y-4)^2 = 3^2

Now you can just read off the center and radius.