First use distance formula to find radius of sphere:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2 + (z_2 -z_1)^2} \\ \\ d = \sqrt{(6-2)^2 + (8-4)^2 + (9-5)^2} \\ \\ d = \sqrt{4^2 +4^2 +4^2} \\ \\ d = 4 \sqrt{3} \\ \\ r =\frac{d}{2} = 2 \sqrt{3}[/tex]
Next, find center of sphere.
The center is located at midpoint between given endponts.
[tex]center = (\frac{2+6}{2}, \frac{4+8}{2},\frac{5+9}{2}) \\ \\ center = (4,6,7)[/tex]
Finally enter values into general equation of sphere:
[tex](x-a)^2 + (y-b)^2 + (z-c)^2 = r^2 \\ \\ (x-4)^2 + (y-6)^2 + (z-7)^2 = 12[/tex]
