if A=(3,5) and B=(4,1).find the equation of locus of point p which are equidistant from points A and B

Answer 1

such a point must lie on the right-bisector of AB
midpoint of AB =(7/2 , 3)
slope of AB = (1-5)/(4-3) = -4
so slope of perpendicular = 1/4

equation:
y-3 = (1/4)(x-7/2)
y - 3 = (1/4)x - 7/8
y = (1/4)x +3 - 7/8
y = (1/4)x + 17/8