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The Day of the Locus (Posted on 2006-12-07) Difficulty: 3 of 5
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)

See The Solution Submitted by Larry    
Rating: 4.0000 (1 votes)

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Solution Solution | Comment 1 of 2

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
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