A variable line passes through a fixed point \(\left(x_{1}, y_{1}\right) \&\) meets the axes at \(A\) and \(B\). If the rectangle OAPB be completed, the locus of \(P\) is, ( \(O\) being the origin of the system of axes)
(A) \(\left(y-y_{1}\right)^{2}=4\left(x-x_{1}\right)\)
(B) \(\frac{x_{1}}{x}+\frac{y_{1}}{y}=1\)
(C) \(x^{2}+y^{2}=x_{1}^{2}+y_{1}^{2}\)
(D) \(\frac{x^{2}}{2 x_{1}^{2}}+\frac{y^{2}}{y_{1}^{2}}=1\)
