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Question

The coordinates of the points O, A and B are (0, 0), (0, 4) and (6, 0) respectively. If a points P moves such that the

area of POA is always twice the area of POB, then the equation to both parts of the locus of P is


A

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B

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C

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D

None of these

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Solution

The correct option is A


The three given points are O(0, 0), A(0, 4) and B(6, 0) and let P(x, y) be the moving point.

Area of POA=2. Area of POB

12×4×x=±2×12×6×y or x=±3y

Hence the equation to both parts of the locus of P is (x - 3y)(x + 3y) = 0.


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