Find the standard equation of the sphere with the given characteristics. endpoints of a diameter: (6, 1, 5), (1, 5, −1)

The first thing we must do for this case, is to find the center of the sphere, for this, we use the following equation:
 
 Substituting values we have:
 
 Rewriting we have:
 
 
 We search now, the radius of the sphere.
 For this, we use the formula of distance between points.
 We have then:
 
 Substituting values we have:
 
 
 Then, the standard equation is given by:
 
 Substituting values:
 
 Rewriting we have:
 
 
 the standard equation of the sphere is:
 

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