The Sum of the Squares of the Distances to N Points

sum of squares of distances

13.4

move the point around the curve

Distances Squared

11.807

1.593

Sum = 13.4

A circle is the locus of points that are a given distance from a given point. An ellipse is the locus of points such that the sum of the distances to two fixed points is constant. What is the locus of points such that the sum of the squares of the distances to two fixed points is constant?