Geometry - Analytic Geometry

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 \(k\).