Question

What is the euqation of the locus of points equidistant from the points (3, 2) and (3, -4)

Answer 1

We need the equation for the distance between the points \[\sqrt{(x _{2}-x_{1})^{2}+(y _{2}-y_{1})^{2}}\]
In this case x1 - x2 =0

Which simplifies nicely to \[y _{2}-y_{1}\]
= -6

Midpoint = (3,-4 + 6/2) = (3,-1)

A locus is essentially a set of points, therefore on any point on the line y=-1 will be equidistant from the two points, A and B. This is the equation of the locus.