Question

Find the radius and center of the given sphere. [Hint: Complete the square in each variable.]

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

Answer 1

Step 1:

The equation of the sphere is  .

The general equation of a sphere with center at and radius is

.

Convert the equation into general equation of sphere :

Add and subtract 2.

 Step 2:

Now compare the obtained equation with general equation of a sphere.

Center

Radius .

Solution:

Center of the sphere and radius of the sphere is .