Answer
$(x−1)^2+(y−2)^2+(z−3)^2=14$
Work Step by Step
First, determine the radius of the sphere using the distance formula:
$d=\sqrt{(x2−x1)^2+(y2−y1)^2+(z2−z1)^2}$
$r=\sqrt{(1-0)^2+(2-0)^2+(3-0)^2}=\sqrt{14}$
The equation for a sphere is represented by:
$(x−h)^2+(y−k)^2+(z−l)^2=r^2$
in which the point $(h,k,l)$ is the center of the sphere and $r$ is the radius.
Plug in the values for the center and the radius.
$(x−1)^2+(y−2)^2+(z−3)^2=14$
