x^2+2x+y^2-2y=9

Question

what is the center and radius of  the circle.

Answer 1

x^2+2x+y^2-2y = 9

To complete squres add (half of x coefficient )^2 and (half of y coefficient )^2 to each side.

x^2+2x+1+y^2-2y+1 = 9+1+1

(x+1)^2+(y-1)^2 = 11

(x-(-1))^2+(y-1)^2 = 11

Compare it to circle equation (x-h)^2+(y-k)^2 = r^2

Center is (h,k) = (-1,1)

Radius(r) = √11 = 3.31