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The coordinates of three points O, A, B ...

The coordinates of three points O, A, B are (0, 0), (0,4) and (6, 0) respectively. A point P moves so that the area of `Delta POA` is always twice the area of `Delta POB`. Find the equation to both parts of the locus of P.

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The correct Answer is:
`x^(2)-9y^(2)=0`
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