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Use mid point formula to find the equation of the sphere in which the segment with endpoints (6, -1, 4) and (-3, 3, 1) is a diameter.

Short Answer

Expert verified

The required equation isx-322+(y-1)2+z-522=532

Step by step solution

01

Given information

A sphere in which the segment with endpoints (6, -1, 4) and (-3, 3, 1) is a diameter.

02

Finding the center and radius

The center, as per mid point formula, is:

6-32,-1+32,4+12

Simplify:

32,1,52

The radius will be half of diameter.

The radius is:

6+32+(-1-3)2+4-122

Simplify:

Radius =1062

03

Finding the equation

The equation of sphere may be written as:

x-322+(y-1)2+z-522=10622

Simplify:

x-322+(y-1)2+z-522=532

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