A variable line intersects co-ordinate axes at two points A and B. If the area of traingle OAB (where 'O' is origin) is 4 square units, then the locus of middle point of AB is-

(1)xy = 2
(2)|xy| = 2
(3)x2?+ y2?= 4
(4)x2?? y2?= 4

Experts the correct answer is option 2 . I'm not getting why the answer with modulus is correct and not option 1 . Please clarify my doubts in detail.