Find an equation of the largest sphere with center (3,3,6) that is contained completely in the first octant.

The equation of a sphere centered at (h, j, k) with radius r is

... (x - h) ² + (y - j) ² + (z - k) ² = r²

The sphere can have a radius no larger than the distance to the nearest octant boundary, one of x=0, y=0, or z=0. That is, the radius must be 3, so the equation is

... (x - 3) ² + (y - 3) ² + (z - 6) ² = 9