Complete the square y^2=4(x+2y)
To complete the square for the given equation y^2 = 4(x + 2y), we need to rearrange the terms to isolate y terms on one side and the constant and x terms on the other side.
y^2 = 4x + 8y
y^2 - 8y = 4x
Next, we complete the square by adding and subtracting the square of half the coefficient of y, which is (8/2)^2 = 16.
y^2 - 8y + 16 = 4x + 16
(y - 4)^2 = 4(x + 4)
Therefore, the equation in completed square form is (y - 4)^2 = 4(x + 4).