Question

Find an equation of the sphere that has radius 1 and center in the first octant and is tangent to each coordinate plane

Answer 1

The distance of the center of the sphere from coordinate planes which it is touching should be equal to radius.

Since the center is in the first octant, then its coordinates are $(1, 1, 1).$ .

The equation of the sphere that has radius 1 and center in the first octant and is tangent to each coordinate plane is

$$(x-1)^2+(y-1)^2+(z-1)^2=1$$