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