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Chapter 10: Q 7 (page 848)

Given a sphere in which the segment with endpoints (1, 5, -2) and (3, 9, -1) is a diameter.

Short Answer

Expert verified

The required equation is:

(x-2)2+(y-7)2+z+322=214

Step by step solution

01

Given information

A sphere with the segment with endpoints (1, 5, -2) and (3, 9, -1) is a diameter.

02

Finding the center and radius

The center may be found using the mid point formula.

The center is:

1+32,5+92,-2-12

Simplify:

2,7,-32

The radius will be half of the diameter. Using the distance formula to find the radius:

12(3-1)2+(9-5)2+(-1-(-2))2

Simplify:

212

03

Writing the equation

The equation of sphere may be written as:

(x-2)2+(y-7)2+z--322=212

Simplify:

(x-2)2+(y-7)2+z+322=214

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