How to find the equation of the sphere with radius $3$ that touches all three coordinate planes in the positive octant?

Question

How to find the equation of the sphere with radius $3$ that touches all three coordinate planes in the positive octant?

Can you help me solve this problem?

Answer 1

There are 8 spheres which are tangent to the coordinate planes. One in each octant. The one in the positive octant is $$(x-3)^2+(y-3)^2+(z-3)^2=3^2.$$ Notice that in general $(x-r)^2+(y-y_0)^2+(z-z_0)^2=r^2$ is a sphere of radius $r$ which is tangent to the plane $x=0$ and which is contained in the half-space $x>0$.

P.S. I assume that "+ve planes" means the coordinate planes: $x=0$, $y=0$ and $z=0$.