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High School Math Calculus Precalculus with Limits: A Graphing Approach

The center and radius of the sphere 9 x 2 + 9 y 2 + 9 z 2 − 18 x + 36 y + 54 z − 126 = 0 .

The center and radius of the sphere 9 x 2 + 9 y 2 + 9 z 2 − 18 x + 36 y + 54 z − 126 = 0 .

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 10.1, Problem 74E

To determine

To find: The center and radius of the sphere 9x2+9y2+9z2−18x+36y+54z−126=0 .

Expert Solution & Answer

Answer to Problem 74E

The center and radius of the sphere 9x2+9y2+9z2−18x+36y+54z−126=0 are (1,−2,−3) and 0 respectively.

Explanation of Solution

Given information:

The equation of the sphere is 9x2+9y2+9z2−18x+36y+54z−126=0 .

Calculation:

The general standard form of the equation of sphere is (x−h)2+(y−k)2+(z−j)2=r2 with center (h,k,j) and r radius.

Simplify the given equation of sphere.

9x2+9y2+9z2−18x+36y+54z−126=09(x2−2x)+9(y2+4y)+9(z2+6z)−126=09(x2−2x+12−12)+9(y2+4y+22−22)+9(z2+6z+32−32)−126=09(x−1)2+9(y+2)2+9(z+3)2−9−36−81−126=0

Further simplify,

9(x−1)2+9(y+2)2+9(z+3)2−9−36−81−126=09(x−1)2+9(y+2)2+9(z+3)2=0(x−1)2+(y+2)2+(z+3)2=0

Compare the equation of sphere (x−1)2+(y+2)2+(z+3)2=0 with general equation. It gives the value of h , k , j as 1 , −2 , −3 respectively and the value of r as 0 .

Therefore, the center and radius of the sphere 9x2+9y2+9z2−18x+36y+54z−126=0 are (1,−2,−3) and 0 respectively.

Chapter 10.1, Problem 73E

Chapter 10.1, Problem 75E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

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