Let \(O\) be the origin, and \(P\) and \(Q\) be two points on the rectangular hyperbola \(xy=12\) such that the midpoint…

Let \(O\) be the origin, and \(P\) and \(Q\) be two points on the rectangular hyperbola \(xy=12\) such that the midpoint of the line segment \(PQ\) is \(\left(\frac{1}{2},-\frac{1}{2}\right)\). Then the area of the triangle \(OPQ\) equals :

[JEE Main 2026, 2 Apr (Shift 2)]