Question

Find an equation of the largest sphere with center (9, 7 , 6) that is contained completely in the first octant.

Answer 1

Well if you think about it, the sphere's radius cannot be any larger than 6 since if it was larger than 6, the sphere would no longer be contained completely in the first octant. So let r=6, x1=9, y1=7, and z1=6. Then using the equation of a sphere we have:
(x-x1)^2 + (y-y1)^2 + (z-z1)^2 = r^2
(x-9)^2+(y-7)^2+(z-6)^2=6^2