Question

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

Answer 1

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