Posted by **Ruth** on Sunday, September 29, 2013 at 1:59am.

Consider two points A=(2,5) and B=(4,3), and a third point P=(a,b) on the x-axis. If the minimum value of line PA^2+ line PB^2 is c, what is a+b+c?

- Algebra -
**Steve**, Sunday, September 29, 2013 at 6:20am
well, b=0 (duh), so

PA^2 = (a-2)^2 + 5^2

PB^2 = (a-4)^2 + 3^2

so you want the minimum value of

(a-2)^2 + 5^2 + (a-4)^2 + 3^2 = 2a^2 - 12a + 54

you know the vertex is at (3,36).

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