Analytic Geometry
posted by xavier .
Please help me to solve this problem.
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.

P(x,y)
m1 = (y3)/(x1)
m2 = (y+2)/(x4)
m1+m2 = 1
(y3)/(x1) + (y+2)/(x4) = 1
(y3)(x4) + (y+2)(x1) = (x4)(x1)
xy  3x 4y+ 12 + xy +2x y 2 = x^25x+4
x^2  4 x 2 xy + 5 y  6 = 0