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High School Math Calculus PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

the standard equation of sphere.

the standard equation of sphere.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 10, Problem 12CR

To determine

To find: the standard equation of sphere.

Expert Solution & Answer

Answer to Problem 12CR

The standard equation of sphere is (x+2)2+(y−6)2+(z+1)2=11 .

Explanation of Solution

Given information:

Endpoints of a diameter: (−3,5,−2),(−1,7,4) .

Formula used: the equation of the sphere with centre and radius,

(x−h)2+(y−k)2+(z−j)2=r2

the distance formula,

d=(x2−x1)2+(y2−y1)2+(z2−z1)2

the midpoint formula,

m=(x1+x22,y1+y22,z1+z22)

Calculation: since, endpoints of diameter are given, the centre of the sphere will be the midpoint of the endpoints of diameter, so to find the centre first substitute in the midpoint formula and then simplify,m=(x1+x22,y1+y22,z1+z22)m=(−3−12,5+72,−2+42) [substitute]m=(−2,6,−1) [simplify]

The radius of the sphere is the half of the distance between of the endpoints of diameter,

d=(x2−x1)2+(y2−y1)2+(z2−z1)2d=(−1+3)2+(7−5)2+(4+2)2 [substitute]d=4+4+36 [subtract,add and square]d=44 [add]d=211

Thus, the radius of sphere is r=11 , to find the equation of sphere, first substitute and then simplify,

(x−h)2+(y−k)2+(z−j)2=r2(x+2)2+(y−6)2+(z+1)2=11 [substitute]

Thus, The standard equation of sphere is (x+2)2+(y−6)2+(z+1)2=11 .

Chapter 10, Problem 11CR

Chapter 10, Problem 13CR

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - 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