Question

In Problems 71–76, find the radius and center of each sphere.

$x^2+y^2+z^2-4x+4y+2z=0$

Short answer

The radius and center of the sphere is$(2,-2,-1)and3$.

Step-by-step solution

Step 1. Given

given equation of the sphere:

$x^2+y^2+z^2-4x+4y+2z=0$

Step 2. Calculation

By applying the standard equation of sphere we get:

$$\begin{gathered} r^2={(x-x_0)}^2+{(y-y_0)}^2+{(z-z_0)}^2 \\ {x}^2+y^2+z^2-4x+4y+2z=0 \\ (x^2-4x)+(y^2+4y)+(z^2+2z)=0 \\ (x^2-4x+4)+(y^2+4y+4)+(z^2+2z+1)=9 \\ {(x-2)}^2+{(y+2)}^2+{(z+1)}^2=9 \\ thereforecenteris(2,-2,-1)andradius3. \end{gathered}$$