Answer
$(x+1)^2+(y-2)^2+(z-4)^2 = 49$
Work Step by Step
We can write the general equation of a sphere:
$(x-a)^2+(y-b)^2+(z-c)^2 = r^2$
where $(a,b,c)$ is the center of the sphere and $r$ is the radius
The center of the sphere is $(-1,2,4)$
The radius of the sphere is $7$
We can find an equation for the sphere:
$(x-a)^2+(y-b)^2+(z-c)^2 = r^2$
$(x-(-1))^2+(y-2)^2+(z-4)^2 = (7)^2$
$(x+1)^2+(y-2)^2+(z-4)^2 = 49$
