x = sqrt{4xy-4y^2}

Squaring both side :

=> x^2 = 4xy - 4y^2

Substituting answer choices, e.g., choice A :

=> (2y)^2 = 4*2y*y - 4y^2

=> 4y^2 - 8y^2 = - 4y^2

So Answer - A

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

=> (x -2y)^2 = 0

=> x = 2y

Note - I thought simplifying further would be faster and more accurate than plugging the answer choices in this case, but situations may vary.

Also, the OA seems to be wrong.

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