Mathematics, 06.05.2020 03:25 Leeyah9587
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 $k$.
I've tried, but got that k = 4x + 18 2/3, which is definitely wrong. I thought to take out the "4x", but its still wrong.
Why is no one helping :(
Answers: 2
![(x-4)^2+(y-(-1))^2+(x-6)^2+(y-2)^2+(x-(-1))^2+(y-2)^2=3[(x-3)^2+(y-1)^2]+k](/tpl/images/0645/7432/f6aef.png)
![RHS:3[(x-3)^2+(y-1)^2]+k\\=3[x^2-6x+9+y^2-2y+1]+k\\=3x^2-18x+27+3y^2-6y+3+k\\=3x^2+3y^2-18x-6y+30+k](/tpl/images/0645/7432/56d3c.png)
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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 th...
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