Let P be (x,y)
PA^2 + PB^2 + PC^2
=(x-4)^2+(y+1)^2+(x-6)^2+(y-2)^2+(x+1)^2+(y-2)^2
=3x^2+3y^2-18x-6y+62
=3(x^2+y^2-6x-2y)+62
=3((x-3)^2+(y-1)^2)+32
This shows that if Q=(3,1), PQ^2=(x-3)^2+(y-1)^2
And so PA^2 + PB^2 + PC^2= 3PQ^2+32
k=32
Hope this helped!!!
