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2014-08-02T21:52:41+05:30

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It is not called equation of P. it is called locus of P (x,y)
AP² = 4 PB²
(x-3)² + (y-0)²  = 4 (x+3)² + 4 (y-0)²
x² -6x +9 +y² = 4 x² + 24x + 36 + 4y²
Take all terms to RHS
3x² + 30x +3y² + 27 = 0  =>  x²+10x + y²+9 = 0


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2014-08-03T11:06:57+05:30
Equation of P. it is called locus of P (x,y)
AP = 2BP
AP² = 4 PB²
using distance formula
⇒(x-3)² + (y-0)²  = 4 (x+3)² + 4 (y-0)²

⇒x² -6x +9 +y² = 4 x² + 24x + 36 + 4y²

3x² + 30x +3y² + 27 = 0 

=>  
x²+10x + y²+9 = 0
so eq of p = 
x²+10x + y²+9 = 0
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