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A variable line passes through a fixed p...

A variable line passes through a fixed point `(x_(1),y_(1))` and 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

`(y-y_(1))^(2)=4(x-x_(1))`

B

`(x_(1))/(x)+(y_(1))/(y)=1`

C

`x^(2)+y^(2)=x_(1)^(2)+y_(1)^(2)`

D

`(x^(2))/(2x_(1)^(2))+(y^(2))/(y_(1)^(2))=1`

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