Question

Find an equation of the sphere that passes through the origin and whose center is (1, -7, 9

Answer 1

The distance between any point on the sphere and its center is the radius. The origin is on the sphere, so the radius $r$ satisfies

$r^2=(1-0)^2+(-7-0)^2+(9-0)^2=131$

This means the equation of the circle is

$(x-1)^2+(y+7)^2+(z-9)^2=131$