Question

Given that A is (-2,-3) and B is (3,4),find the equation of the locus of the point in the x–y plane,moving under the condition that PA=PB.?

Answer 1

Point P lies on the perpendicular bisector of AB.

The midpoint of AB is (1/2, 1/2)
The slope of AB is 7/5, so the perpendicular bisector has slope -5/7
So, now you have a point and a slope. The given locus has equation
y - 1/2 = -5/7 (x - 1/2)