Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant? Describe process.

The radius must not exceed the smallest coordinate, i. e. 4. This gurantees the the sphere will not leave the first octant.

Then the largest radius is 4, and the equation is

(x-5) ^2 + (y-4) ^2 + (z-9) ^2 = 4^2

(x-5) ^2 + (y-4) ^2 + (z-9) ^2 = 16