Answer
$(x-5)^{2}+(y-4)^{2}+(z-9)^{2}=16$
Work Step by Step
The largest sphere contained in the first octant must have a radius equal to the minimum distance from the center (5,4,9) to
any of the three coordinate planes. The shortest such distance is to the xz-plane, a distance of 4. Thus an equation of the
sphere is $(x-5)^{2}+(y-4)^{2}+(z-9)^{2}=16$.
