Answer
See the verification below.
Work Step by Step
Let $(a,b,c)$ be the center of the sphere, $(x,y,z)$ be an arbitrary point of the sphere, and $r$ be the distance between $(a,b,c)$ and $(x,y,z)$. Then, using the Pythagorean Theorem, the standard form of the equation of the sphere can be expresses as:
$r=\sqrt {(x-a)^2+(y-b)^2+(z-c)^2}$
or, squaring both sides
$(x-a)^2+(y-b)^2+(z-c)^2=r^2$
This shows an equation of the sphere with radius $r$ and center at $(a,b,c)$.
