Problem: Given an equilateral triangle with side of length s, consider the locus of all points P in the plane of the triangle such that the sum of the squares of the distances from P to the vertices of the triangle is a fixed number a. This locus
Answer Choices:
A. is a circle if a>s2
B. Contains only three points if a=2s2 and is a circle if a>2s2
C. Is a circle with positive radius only if s2<a<2s2
D. Contains only a finite number of points for any value of a
E. Is none of these
Solution:
Let point P have coordinates (x,y) in the coordinate system in which the vertices of the equilateral triangle are (0,0),(s,0) and (s/2,s3​/2). Then P belongs to the locus if and only if