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

Tofind: The equation of sphere whose end points of diameter are given. Also, to sketch the sphere and the xz- plane.

Tofind: The equation of sphere whose end points of diameter are given. Also, to sketch the sphere and the xz- plane.

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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Concept explainers

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Question

Chapter 10, Problem 4CT

To determine

Tofind:The equation of sphere whose end points of diameter are given. Also, to sketch the sphere and the xz- plane.

Expert Solution & Answer

Answer to Problem 4CT

The equation of sphere is (x−7)2+(y−1)2+(z−2)2=19 . The graph of sphere and xz-plane is shown in Figure-2.

Explanation of Solution

Given information:

The end points of the diameter of the sphere are A(8,−2,5) and B(6,4,−1)

Formulaused:

The midpoint of diameter is the center of the sphere. The coordinates of mid-point of line segment joining points (x1,y1,z1) and (x2,y2,z2) are x=x1+x22 , y=y1+y22 , and z=z1+z22 ,

Calculations:

The end points of diameter of the sphere are A(8,−2,5) , and B(6,4,−1) . The midpoint of the diameter is the center (xC,yC,zC) of the sphere given by

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 10, Problem 4CT , additional homework tip 1

xC=8+62=7 , yC=−2+42=1 , zC=5−12=2 .

The radius Rof the sphereis PC=AC=CB .

The radius of the sphere R=AC=12AB=12(6−8)2+(4−(−2))2+(−1−5)2

⇒R=AC=12AB=124+36+36

⇒R=1276=12219=19

Let P(x,y,z) be a point on the sphere then PA=R

(x−7)2+(y−1)2+(z−2)2=19

⇒(x−7)2+(y−1)2+(z−2)2=19

Thus, the equation of sphere is (x−7)2+(y−1)2+(z−2)2=19 .

The diagram of sphere is shown in Figure (b) here.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 10, Problem 4CT , additional homework tip 2

Conclusion:

The equation of sphere is (x−7)2+(y−1)2+(z−2)2=19 . The graph of sphere and xz-plane is shown in Figure-2.

Chapter 10, Problem 3CT

Chapter 10, Problem 5CT

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

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