#### Answer

$(x+2)^2 + y^2 + (z-4)^2 \leq 1^2$

#### Work Step by Step

Equation of sphere with radius $r$ and centered at $(a,b,c)$:
$(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2$
Plug in center and radius:
$(x+2)^2 + (y-0)^2 + (z-4)^2 = 1^2$
Because it's a ball, the equation must account for the fact that the sphere is not hollow.
$(x+2)^2 + (y-0)^2 + (z-4)^2 \leq 1^2$