Consider the sphere with center $\backslash ((9,-7,5)\backslash )$ and contains the point $\backslash ((3,-4,3)\backslash ).$ Find the equation of the sphere, and then for each coordinate plane, determine whether or not the sphere intersects the plane. If it does intersect, describe the intersection $($by giving both an equation representing the intersection and a specific description of the intersection$).$ If the sphere does not intersect that plane, find the exact minimum distance from the sphere to the plane.

a$.$ Find the equation of the sphere:

b$.$ Intersection with the $\backslash ($ x y $\backslash )-$plane:

c$.$ Intersection with the $\backslash ($ x z $\backslash )-$plane:

d$.$ Intersection with the $\backslash ($ y z $\backslash )-$plane: