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Question

The locus of the moving point P such that 2PA=3PB, where A is (0,0) and B is (4,3), is

A
5x2+5y2+72x+54y+225=0
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B
5x2+5y272x54y+225=0
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C
5x2+5y272x+54y+225=0
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D
5x2+5y272x+54y225=0
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Solution

The correct option is C 5x2+5y272x+54y+225=0
Let the coordinates of the point P be (α,β).
Then, we have
2PA=3PB4PA2=9PB2
4[(α0)2+(β0)2]=9[(α4)2+(β+3)2]
5α2+5β272α+54β+225=0
The locus of P is 5x2+5y272x+54y+225=0

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