Find the equation of the sphere passing through P(-4,7,6) and Q(6, -5,7) with its center at the midpoint of PQ. The standard equation of the sphere is. (Simplify your answer.)

The standard equation of the sphere is .

Step-by-step explanation:

The distance between the points and is

The midpoint between the points and is

Midpoint =

A sphere is the set of all points that are a constant distance from a point ; is the radius of the sphere, and is the center of the sphere.

A sphere centered at with radius is the set of points satisfying the

equation

To find the equation of the sphere passing through and with its center at the midpoint of .

The center of the sphere is the midpoint of :

The diameter of the sphere is the distance , which is

Therefore, the sphere’s radius is , its center is , and it is described by the equation