Question

Area of the region that consists of all the points satisfying the conditions |x - y| + |x + y| ≤ 8 and xy ≥ 2 is equal to 

(A) 4(7 - ln 8) sq. units 

(B) 4(9 - ln 8) sq. units 

(C) 2(7 - ln 8) sq. units 

(D) 2(9 - ln 8) sq. units

Answer 1

Answer is (A) 4(7 - ln 8) sq. units

See Fig.

The expression |x - y| + |x + y| ≤ 8, represents the interior region of the square formed by the lines x = ±4, y = ±4 and xy ≥ 2. Represents the region lying inside the hyperbola xy =2. Required area is