Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 5 x = 0$
A)Center: $\left( \frac { 5 } { 2 } , 0,0 \right)$ Radius: $\frac { 5 } { 2 }$
B)Center: $\left( 0 , \frac { 3 } { 2 } , 0 \right)$ Radius: $\frac { 3 } { 2 }$
C)Center: $\left( 0 , \frac { 3 } { 2 } , \frac { 1 } { 2 } \right)$ Radius: $\frac { \sqrt { 10 } } { 2 }$
D)Center: $\left( \frac { 1 } { 2 } , 0,0 \right)$ Radius: $\frac { 1 } { 2 }$
E)Center: $\left( \frac { 5 } { 2 } , 0,1 \right)$ Radius: $\frac { \sqrt { 29 } } { 2 }$

Question

Quizplus · Accepted Answer

To find the center and radius of the sphere given by the equation $x^2 + y^2 + z^2 - 5x = 0$, we need to complete the square for the $x$-term. Completing the square involves adding and subtracting $\left(\frac{5}{2}\right)^2 = \frac{25}{4}$ inside the equation, leading to $x^2 - 5x + \frac{25}{4} + y^2 + z^2 = \frac{25}{4}$. This can be rewritten as $(x - \frac{5}{2})^2 + y^2 + z^2 = \left(\frac{5}{2}\right)^2$, indicating a sphere with center $\left(\frac{5}{2}, 0, 0\right)$ and radius $\frac{5}{2}$.

Find the Center and Radius of the Sphere x2+y2+z2−5x=0x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 5 x = 0x2+y2+z2−5x=0

Find the Center and Radius of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 5 x = 0$