The line \(A B\) cuts off equal intercepts 2 a from the axes. From any point \(P\) on the line \(A B\) perpendiculars \(P R\) and \(P S\) are drawn on the axes. Locus of mid-point of RS is
(A) \(x-y=\frac{a}{2}\)
(B) \(x+y=a\)
(C) \(x^{2}+y^{2}=4 a^{2}\)
(D) \(x^{2}-y^{2}=2 a^{2}\)
