(688,#25) Find equations of the spheres with center (2,-3,6) that touch

(688,#25) Find equations of the spheres with center (2,-3,6) that touch (a) the xy plane, (b) yz plane,
(c) the xz plane.
Solution:
a) If the center is (2,-3,6), the sphere's distance to the xy plane would be the distance z, therefore the radius of the sphere would be the distance z = r = 6.
If the equation of the sphere with center C(h,k,l) and radius r:

The equation of the sphere is:

b) If the center is (2,-3,6), the sphere's distance to the yz plane would be the distance x, therefore, the radius of the sphere would be the distance x = r = 2.
The equation of the sphere is:

c) If the center is (2,-3,6), the sphere's distance to the xz plane would be the distance y, therefore, the radius of the sphere would be the distance y = r = 3.
The equation of the sphere is:

by:sh