A moving line intersects the lines \(x+y=0\) and \(x-y=0\) at the points \(A, B\) respectively such that the area of the triangle with vertices \((0,0), A \& B\) has a constant area \(C\). The locus of the mid-point \(A B\) is given by the equation
(A) \(\left(x^{2}+y^{2}\right)^{2}=C^{2}\)
(B) \(\left(x^{2}-y^{2}\right)^{2}=C^{2}\)
(C) \((x+y)^{2}=C^{2}\)
(D) \((x-y)^{2}=C^{2}\)
Ans(B)
