find the equation of the locus of the point which moves such that the ratio of the distances from (2,0)and (1,3)is 5:4

then, acc. to distance formula,

PA = [(x - 2)^{2} + (y-0)^{2}]^{1/2}

PB = [(x - 1)^{2} + (y-3)^{2}]^{1/2}

given, PA/PB = 5/4

PA^{2}/PB^{2 }= 25/16

(x - 2)^{2} + (y-0)^{2} / (x - 1)^{2} + (y-3)^{2 } = 25/16

x^{2}+4-4x + y^{2} / x^{2}+1-2x + y^{2}+9-6y = 25/16

16x^{2}+64-64x +16 y^{2} = 25x^{2}+25-50x + 25y^{2}+225-150y

on solving we get,

9x^{2} + 9y^{2} + 14x -150y + 186 = 0

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