Let \(A = (4,-1), B = (6,2)\), and \(C = (-1,2)\). There exists a point \(X\) and a constant \(k\) such that for any point \(P\),
\(PA^2 + PB^2 + PC^2 = 3PX^2 + k.\)
Find the constant \(k\).
CPhill, I'm not sure how to solve this, can you solve it?
X = (-2,5) and k = 44.