Answer
$(x-1)^2+(y-2)^2+(z-3)^2 = 25$
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 $(1,2,3)$
We can find the radius of the sphere:
$r = \sqrt{(5-1)^2+(5-2)^2+(3-3)^2}$
$r = \sqrt{(4)^2+(3)^2+(0)^2}$
$r = \sqrt{16+9+0}$
$r = \sqrt{25}$
The radius of the sphere is $5$
We can find an equation for the sphere:
$(x-a)^2+(y-b)^2+(z-c)^2 = r^2$
$(x-1)^2+(y-2)^2+(z-3)^2 = (5)^2$
$(x-1)^2+(y-2)^2+(z-3)^2 = 25$
