Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 4 - 8 y = 0$
A) $C ( 2,2,4 ) ; r = \sqrt { 2 }$
B) $C ( 0,2,4 ) ; r= 4$
C) $C ( 2,4,0 ) ; r = \sqrt { 2 }$
D) $C ( 2,4,0 ) ; r= 2$
E)none of these

Question

Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 4 - 8 y = 0$
A) $C ( 2,2,4 ) ; r = \sqrt { 2 }$ 
B) $C ( 0,2,4 ) ; r= 4$ 
C) $C ( 2,4,0 ) ; r = \sqrt { 2 }$ 
D) $C ( 2,4,0 ) ; r= 2$ 
E)none of these

Quizplus · Accepted Answer

The given equation is $x^2 + y^2 + z^2 - 4x - 8y = 0$. To find the center and radius, we complete the squares for $x$, $y$, and $z$. The equation can be rewritten as $(x^2 - 4x) + (y^2 - 8y) + z^2 = 0$. Completing the square for $x$ and $y$ gives $(x - 2)^2 - 4 + (y - 4)^2 - 16 + z^2 = 0$, or $(x - 2)^2 + (y - 4)^2 + z^2 = 20$. Thus, the center is $(2, 4, 0)$ and the radius is $\sqrt{20}$, which is not listed among the options.

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

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