Find an equation of the sphere with center (−2, 3, 7) and radius 7.What is the intersection of this sphere with the yz-plane?

The equation of the sphere with center (-2, 3, 7) and radius 7 is .

The intersection of the sphere with the yz-plane is .

Step-by-step explanation:

We know that any sphere can be represented by the following equation:

Where:

, , - Coordinates of the center of the sphere, dimensionless.

- Radius of the sphere, dimensionless.

If and , we obtain this expression:

The intersection of the sphere with the yz-plane observe the following conditions:

, ,

Hence, the expression above can be reduced into this: