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Chapter 10: Q 36 (page 789)

Use the midpoint formula to find the equations of the sphere in which the segment with endpoints (3, 鈭�2, 6) and (5, 6, 4) is a diameter.

Short Answer

Expert verified

The required equation is(x-4)2+(y-2)2+(z-5)2=18

Step by step solution

01

Given information

A sphere in which the segment with endpoints (3, 鈭�2, 6) and (5, 6, 4) is a diameter.

02

Finding the radius and center

The radius is half of diameter which is half of the distance between the two endpoints given.

Radius is:

12(5-3)2+(6+2)2+(4-6)2

Solving:

Radius is 32

The center, as per mid point formula, is:

5+32,6-22,4+62

Simplify:

4,2,5

03

Writing the equation

The equation of sphere is:

(x-4)2+(y-2)2+(z-5)2=(32)2

Simplify:

(x-4)2+(y-2)2+(z-5)2=18

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