What is the Locus of a point that moves in such a way that it's sum of the squares of the distance (with weight factors) to N fixed points remains constant?
Use Applet to visualise that, in this case, the locus is a circle and check that the sum of the squares of the distances (with weight factors) to the N fixed points remains constant. The locus turns out to be a circle with its center in the center of “gravity” of the system of “charged” points.
The algebraic sum of the squares of the distances, qi*|x - xi|², is analogous to electrostatics. In this analogy, qi is added to the formulas as a real values, or weight factors.
*Click the Update button until a green circle appears in the plane of the screen.
Example of distribution of charged particles
