look to the coefficients on the middle terms (-4x and 2y)
divide each coefficient by 2 and square to determine what to add.
(-4/2)^2 = 4 needs to be added to complete the square for x.
(2/2)^2 = 1 needs to be added to complete the square for y.
add to both sides of the equal sign to keep the equation balanced.
x^2 - 4x + 4 + y^2 + 2y + 1 = b + 4 + 1
factor
(x - 2)^2 + (y + 1)^2 = b + 5
The general equation for a circle is:
(x - h)^2 + (y - k)^2 = r^2
with center (h,k) and radius r
compare this to the equation. you see that the center is: (2, -1)
we can write
r^2 = b + 5
given that r = 7
49 = b + 5
49 - 5 = b
44 = b
