Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 5 x = 0$
A)Center: $\left( \frac { 25 } { 4 } , 0,0 \right)$ Radius: $\frac { 5 } { 2 }$
B)Center: $\left( \frac { 5 } { 2 } , 0,0 \right)$ Radius: $\frac { 5 } { 2 }$
C)Center: $\left( - \frac { 5 } { 2 } , 0,0 \right)$ Radius: $\frac { 5 } { 2 }$
D)Center: $\left( \frac { 5 } { 2 } , 5,0 \right)$ Radius: $\frac { 5 } { 2 }$
E)Center: $\left( \frac { 25 } { 4 } , 0,5 \right)$ Radius: $\frac { 5 } { 2 }$

Question

Find the center and radius of the sphere.  $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 5 x = 0$ 
A)Center: $\left( \frac { 25 } { 4 } , 0,0 \right)$ Radius: $\frac { 5 } { 2 }$
B)Center: $\left( \frac { 5 } { 2 } , 0,0 \right)$ Radius: $\frac { 5 } { 2 }$
C)Center: $\left( - \frac { 5 } { 2 } , 0,0 \right)$ Radius: $\frac { 5 } { 2 }$
D)Center: $\left( \frac { 5 } { 2 } , 5,0 \right)$ Radius: $\frac { 5 } { 2 }$
E)Center: $\left( \frac { 25 } { 4 } , 0,5 \right)$ Radius: $\frac { 5 } { 2 }$

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 complete the square for the $x$ term. The equation can be rewritten as $x^2 - 5x + y^2 + z^2 = 0$. Adding and subtracting $\left(\frac{5}{2}\right)^2$ (which is $\frac{25}{4}$) to complete the square for $x$, we get $x^2 - 5x + \frac{25}{4} + y^2 + z^2 = \frac{25}{4}$. This simplifies to $\left(x - \frac{5}{2}\right)^2 + y^2 + z^2 = \left(\frac{5}{2}\right)^2$. Thus, the center is $\left(\frac{5}{2}, 0, 0\right)$ and the radius is $\frac{5}{2}$.

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 $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 5 x = 0$