Question

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

Short answer

The radius and center of the sphere is

$(-1,1,0)and2$.

Step-by-step solution

Step 1. Given

given equation of the sphere:

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

Step 2. Calculation

By applying the standard equation of sphere we get:

$$\begin{gathered} r^2={(x-x_0)}^2+{(y-y_0)}^2+{(z-z_0)}^2 \\ {x}^2+y^2+z^2+2x-2y=2 \\ (x^2+2x)+(y^2-2y)+z^2=2 \\ (x^2+2x+1)+(y^2-2y+1)+z^2=2+1+1 \\ {(x+1)}^2+{(y-1)}^2+z^2=4 \\ thereforecenteris(-1,1,0) \\ andradiusis2 \end{gathered}$$