Answer
$$(x-1)^2+(y-3)^2+z^2=10$$
Work Step by Step
Endpoints of the diameter are $(2,0,0)$ and $(0,6,0)$. The center of the sphere is therefore the midpoint of these two points.
Center=$\left(\frac{2+0}{2},\frac{0+6}{2},\frac{0+0}{2}\right)=(1,3,0)$. The radius is $\frac{1}{2}\times$distance between the two points.
$r=\frac{1}{2}\sqrt{(2-0)^2+(0-6)^2+(0-0)^2}=\frac{1}{2}\sqrt{40}=\frac{1}{2}\times2\sqrt{10}=\sqrt{10}$ The equation of the sphere is therefore
$(x-1)^2+(y-3)^2+(z-0)^2=\sqrt{10}^2$
=$$(x-1)^2+(y-3)^2+z^2=10$$
