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Find the equation of the locus of a moving point such that the slope of the line joining the point to A(1,3) is three times the slope of the line joining the point to B(3,1).

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  1. let the point be P(x,y)
    slope AP = (y-3)/(x-1)
    slope BP = (y-1)/(x-3)
    (y-3)/(x-1) = 3(y-1)/(x-3)
    xy - 3y - 3x + 9 = 3xy -3y - 3x + 3
    2xy = 6

    xy = 3

    Test for reasonableness :
    I know P(12, 1/4) lies on it

    slope AP = (1/4 - 3)/(12-1)
    = -1/4
    slope BP = (1/4 - 1)/(12-3)
    = -1/12

    and -1/4 = 3(-1/12) , as needed

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