In coordinate space, find the sum of all real numbers $k$ such that the plane $x + 8 y - 4 z + k = 0$ is tangent to the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 2 y - 3 = 0$. [3 points]
In coordinate space, find the sum of all real numbers $k$ such that the plane $x + 8 y - 4 z + k = 0$ is tangent to the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 2 y - 3 = 0$. [3 points]