In the coordinate plane, A=(4,-1), B=(6,2), and C=(-1,2). There exists a point Q and a constant k such that for any point P,

In the coordinate plane, A=(4,-1), B=(6,2), and C=(-1,2). There exists a point Q and a constant k such that for any point P,

 

PA^2 + PB^2 + PC^2 = 3PQ^2 + k

 

Find the constant k.

 

 

I know this was asked already, but I couldn't figure it out. Thanks!