Question

In Problems 71–76, find the radius and center of each sphere.
$x^2+y^2+z^2+2x-2z=-1$

Short answer

The radius and center of the sphere is

$(-1,0,1)and1$.

Step-by-step solution

Step 1. Given

given equation of the sphere:

$x^2+y^2+z^2+2x-2z=-1$

Step 2. Calculation

By applying the standard equation of sphere we get:

$$\begin{gathered} r^2={(x-x_0)}^2+{(y-y_0)}^2+{(z-z_0)}^2 \\ {x}^2+y^2+z^2+2x-2z=-1 \\ (x^2+2x)+y^2+(z^2-2z)=2 \\ (x^2+2x+1)+y^2+(z^2-2z+1)=-1+1+1 \\ {(x+1)}^2+y^2+{(z-1)}^2=1thereforecenteris(-1,0,1) \\ andradiusis1 \end{gathered}$$