Answer to Question #166775 in Analytic Geometry for Anshiks

Question

Find the equation of the spheres of radius r which touch the three coordinate axis . How many such sphereshort are there?

Answer 1

Let the radius of the sphere be r; then the distance of its center from coordinate planes which it is touching should be equal to radius a.

Hence, its center is (r,r,).

But since the center can be in any octant, we say that its center is (±r,±r,±r) and radius r, so that its equation is 

$(x±)^2+(y±a)^2+(z±a)^2=a^2\\ ⇒x^2+y^2+z ^2±2rx±2ry±2rz+2r^2 =0\\ Also, \\ \text{There are 8 quadrant in 3D, so for a given radius there will be 8 possible sphere touching all the 3 coordinate planes.}$