Find an equation of the sphere that passes through the origin and whose center is (6,-7,7).

The equation of a sphere of radius r with centre at (a, b, c) is

(x-a) ^2 + (y-b) ^2 + (z-c) ^2=r^2

Thus with (a, b, c) = (6,-7,7), the equation of the sphere is

(x-6) ^2 + (y+7) ^2 + (z-7) ^2=r^2