Question

Find an equation of the largest sphere with center (8, 2, 9) that is contained in the first octant.

Answer 1

The point (8,2,9) is in the first octant.
The closest distance from the coordinate planes is the value y=2, which will therefore be the maximum radius of the required sphere.

The standard equation of a sphere with radius r and centre (u,v,w) is given by
(x-u)^2+(y-v)^2+(z-w)^2=r^2

Substituting r=2, u=8, v=2, w=9, we get the equation of the required sphere
(x-8)^2+(y-2)^2+(w-9)^2=2^2