Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x = 0$
A)Center: $( 2,0 , - 2 )$ Radius: $2$
B)Center: $( 2,2,2 )$ Radius: $2$
C)Center: $( 2,0,2 )$ Radius: $2$
D)Center: $( 2,0,0 )$ Radius: $2$
E)Center: $( 2 , - 2,0 )$ Radius: $2$

Question

Find the center and radius of the sphere.  $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x = 0$ 
A)Center: $( 2,0 , - 2 )$ Radius: $2$
B)Center: $( 2,2,2 )$ Radius: $2$
C)Center: $( 2,0,2 )$ Radius: $2$
D)Center: $( 2,0,0 )$ Radius: $2$
E)Center: $( 2 , - 2,0 )$ Radius: $2$

Quizplus · Accepted Answer

To find the center and radius of the sphere given by the equation $x^2 + y^2 + z^2 - 4x = 0$, we complete the square for the $x$ term. The equation can be rewritten as $(x^2 - 4x) + y^2 + z^2 = 0$. Completing the square for the $x$ term involves adding and subtracting $(4/2)^2 = 4$, so we get $(x^2 - 4x + 4) + y^2 + z^2 = 4$, which simplifies to $(x - 2)^2 + y^2 + z^2 = 2^2$. This shows the center of the sphere is at $(2, 0, 0)$ and the radius is $2$.

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

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