   Chapter 7.5, Problem 6QY ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Find the center and radius of the sphere whose equation is x 2 + y 2 +   z 2 − 8. t   − 2 y   —   6 z   — 23   =   0.

To determine

To calculate: The centre and radius of the sphere who’s the equation of a sphere is x2+y2+z28x2y6z23=0.

Explanation

Given Information:

The equation of a sphere is x2+y2+z28x2y6z23=0.

Formula used:

The standard form of a sphere is,

(xa)2+(yb)2+(zc)2=r2

Where, (a,b,c) is centre of sphere and r is radius of sphere.

Calculation:

Considering the primary equation of sphere as,

(xa)2+(yb)2+(zc)2=r2

Where (a,b,c) is centre of sphere and r is radius.

Now consider the secondary equation

x2+y2+z28x2y6z23=0

Simplifying the above equation to form a standard form of equation of sphere,

x2+(3x)2+y2(2y)z26z23=0(x22(4x)+42)42+

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