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
let the point be P(x,y) and the points A(2,0) and B(1,3)
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
PA2/PB2 = 25/16
(x - 2)2 + (y-0)2 / (x - 1)2 + (y-3)2 = 25/16
x2+4-4x + y2 / x2+1-2x + y2+9-6y = 25/16
16x2+64-64x +16 y2 = 25x2+25-50x + 25y2+225-150y
on solving we get,
9x2 + 9y2 + 14x -150y + 186 = 0