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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 \(k\).

 Mar 30, 2020
 #1
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CPhill, I'm not sure how to solve this, can you solve it?

 Mar 30, 2020
 #2
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X = (-2,5) and k = 44.

 Mar 31, 2020

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