The distance between any point on the sphere and its center is the radius. The origin is on the sphere, so the radius [tex]r[/tex] satisfies
[tex]r^2=(1-0)^2+(-7-0)^2+(9-0)^2=131[/tex]
This means the equation of the circle is
[tex](x-1)^2+(y+7)^2+(z-9)^2=131[/tex]
