What is the locus of points that are exactly n times farther from P2 than from P1?

(P1 and P2 are two points in the x-y plane, and n is a positive real number)

If n = 1, then the locus is the perpendicular
bisector of the line segment P1P2; otherwise,
the locus is the circle with diameter AB. Where

 P1, A, P2, and B are collinear and

  P1A                    P1B            
 ----- = n      and     ----- = -n
  AP2                    BP2           

[Note: line segments are directed]

Posted by Bractals on 2006-12-07 10:30:49