2. Consider the spherical surface with equation $( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } + z ^ { 2 } = 1$ and the plane $\pi$ with equation $x - 2 y - 2 z + d = 0$. Discuss, as the real parameter $d$ varies, whether the plane $\pi$ is secant, tangent or external to the spherical surface. Determine the value of the parameter $d$ so that $\pi$ divides the sphere into two equal parts.