Question

Show that the equation represents a sphere, and find its center and radius.

 

Answer 1

Step 1:

The equation is .

Rewrite the expression.

Take out 2 as a common factor.

Divide each side by 2.

Group the terms.

Complete the each square.

Compare the above equation with equation of the sphere .

Where is the center of the sphere.

r  is the radius of the sphere.

So represents the equation of the sphere.

Here and .

Solution :

The center of the sphere is .

The radius of the sphere is .