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?
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).