Equidistant line from two fixed points
Each point P in turn on the red line is equidistant from points X and Y.
The red line represents the locus of points equidistant from X and Y.

Equidistant line from a fixed point(a circle)
All the points P lie on a locus of points the same distance from O (i.e on the perimeter of the circle)

Equidistant line from two lines joined at a vertex
Each point P in turn on the red line is equidistant from lines OX and OY.
The red line represents the locus of points equidistant from lines OX and OY.

Contact GCSE Maths Tutor here - info@gcsemathstutor.com