Lets take line AB as x axis with origin at its mid point.
So general co-ordinates f A abd B can be give as (-k,0) and (k,0)
Now line bisecting AB and perpendicular to it is y axis.
You have to show that any point on y axis is equi distant feom point a and point B.
Any point on y axis can e denoted as (0,p)
so distance of tis point from A is
Distance of same point from B is
Hence this point of y axis is at equal distance from A and B.