Find the equation of the sphere passing through pleft parenthesis negative 2 comma 3 comma 4 right parenthesis(−2, 3, 4) and qleft parenthesis 8 comma negative 1 comma 5 right parenthesis(8, −1, 5) with its center at the midpoint of pq.

In  this question , the given points are

Center is at the midpoint of PQ . And to find the midpoint, we will use the following formula

Substituting the points in the formula, we will get

And PQ gives the diameter, and to find the length of diameter, we will use the following formula

Substituting the given values, we will get

Radius is half of diameter, that is

Now we use the equation of sphere, which is

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