It appears that the above equations can be reorganized a bit to make it easy for the further processing:

x = sqrt(4xy - 4y^2)

x^2 = 4xy - 4y^2

x^2 - 4xy + 4y^2 = 0

(x-2y)^2 = 0

x- 2y = 0

x = 2y

Answer is A

Given that x = sqrt(4xy - 4y^2)
square both side, we have
x^2 = 4xy - 4y^2
The above equation can be rewritten as
x^2 - 4xy - 4y^2= 0
Mathematically,
(x-2y)^2 = x^2 - 4xy - 4y^2
we can rewrite (x-2y)^2=0
square both side, we have x-2y = 0
i.e eliminating the square at the left hand side of the equation.
x-2y = 0
x=2y

option A is correct