Answer
$x^2+y^2+z^2 = 178$
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 $(0,0,0)$
We can find the radius of the sphere:
$r = \sqrt{(3-0)^2+(12-0)^2+(-5-0)^2}$
$r = \sqrt{(3)^2+(12)^2+(-5)^2}$
$r = \sqrt{9+144+25}$
$r = \sqrt{178}$
The radius of the sphere is $\sqrt{178}$
We can find an equation for the sphere:
$(x-a)^2+(y-b)^2+(z-c)^2 = r^2$
$(x-0)^2+(y-0)^2+(z-0)^2 = (\sqrt{178})^2$
$x^2+y^2+z^2 = 178$
