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If the distance from P to the points (5, -4), (7, 6) are in the ratio 2 : 3, then the locus of P is

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$5 x^{2} + 5 y^{2} - 12 x - 86 y + 17 = 0$

$5 x^{2} + 5 y^{2} - 5 x + y + 29 = 0$

$3 x^{2} + 3 y^{2} - 20 x + 38 y + 87 = 0$

$5 x^{2} + 5 y^{2} - 34 x + 120 y + 29 = 0$

answer is B.

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Detailed Solution

$A (5, - 4) . B (7, 9); 3 P A = 2 P B$

$9 P A^{2} = 4 P B^{2}$

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