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

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$3 x^{2} + 3 y^{2} - 70 x + 52 y + 225 = 0$

$5 x^{2} + 5 y^{2} + 72 x - 54 y - 225 = 0$

$5 x^{2} + 5 y^{2} - 72 x - 54 y + 225 = 0$

$3 x^{2} - 3 y^{2} - 8 x + 16 y + 20 = 0$

answer is A.

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Detailed Solution

$\frac{PA}{PB} = \frac{3}{2} \Rightarrow 4 {PA}^{2} = 9 {PB}^{2}$

$4 [{(x - 0)}^{2} + {(y - 0)}^{2}] = 9 [{(x - 4)}^{2} + {(y - 3)}^{2}] 4 x^{2} + 4 y^{2} = 9 x^{2} + 9 y^{2} - 72 x - 54 y + 225 5 x^{2} + 5 y^{2} - 72 x - 54 y + 225 = 0$

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