Math (or geometry) problem... Involving points.

CBlair1986_at_aol.com
Date: 01/21/05 

Date: 20 Jan 2005 20:52:16 -0800

Given two points on a plane, (x1,y1) and (x2,y2), is there any possible
way to find the coordinates of the points that are a unit away from
both point 1 and point 2?

Also, would it be possible to do this in three dimensions as well?
Thanks all.