Find the center and the radius of the sphere that has the given equation.
$$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 8 y = 0$$
A) $( 2 , - 4,0 ) , 2 \sqrt { 5 }$
B) $( - 2,4,0 ) , 20$
C) $( - 2,4,0 ) , 2 \sqrt { 5 }$
D) $( 2 , - 4,0 ) , 20$

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the form $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$ by completing the square. Completing the square for $x$ and $y$, we get $(x - 2)^2 + (y + 4)^2 + z^2 = 20$. Thus, the center is $(2, -4, 0)$ and the radius is $\sqrt{20} = 2\sqrt{5}$.

Find the Center and the Radius of the Sphere That x2+y2+z2−4x+8y=0x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 8 y = 0x2+y2+z2−4x+8y=0

Find the Center and the Radius of the Sphere That $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 8 y = 0$