Question

A sphere S laying in the first octant has its center C in the plane with equation z=5 and is tangent to the xz-plane and to the yz-plane. The distance from the origin to C is sqrt(43).
a.) Find an equation for S of the form (x-a)^2 + (y-b)^2 + (z-c)^2=r^2.
b.) Find the distance between the origin and the point where S touches the xz-plane.