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Question

If A=(5,0) and B=(0,4), then the locus of moving point P such that |PA|2|PB|2=9 is

A
5x4y=0
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B
4x5y=0
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C
5x+4y=0
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D
4x+5y=0
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Solution

The correct option is A 5x4y=0
Let P(x,y) be an arbitrary point satisfying the condition.Then we have |PA|2|PB|2=9
((x5)2+y2)(x2+(y4)2)=9
10x+25+8y16=9
5x4y=0
Hence, the equation of the locus of P is 5x4y=0

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