# Analytic Geometry

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Find the equation of the locus of a moving point if the sum of the slopes of the line joining it to (1,3) and (4,-2) is 1.

• Analytic Geometry -

P(x,y)
m1 = (y-3)/(x-1)
m2 = (y+2)/(x-4)
m1+m2 = 1
(y-3)/(x-1) + (y+2)/(x-4) = 1

(y-3)(x-4) + (y+2)(x-1) = (x-4)(x-1)

xy - 3x -4y+ 12 + xy +2x -y -2 = x^2-5x+4

x^2 - 4 x -2 xy + 5 y - 6 = 0

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