Explanation Given: The equation is 4 x 2 + 4 y 2 + 4 z 2 − 24 x − 4 y + 8 z − 23 = 0 . Formula used: The equation of sphere is ( x − l ) 2 + ( y − m ) 2 + ( z − m ) 2 = r 2 where ( l , m , n ) are the center points and r is the radius. The formula from algebra is: ( a + b ) 2 = a 2 + 2 a b + b 2 ( a − b ) 2 = a 2 + b 2 − 2 a b Calculation: Consider the equation 4 x 2 + 4 y 2 + 4 z 2 − 24 x − 4 y + 8 z − 23 = 0 . Divide by 4, x 2 + y 2 + z 2 − 6 x − y + 2 z − 23 4 = 0 Then, group the same variable terms. x 2 − 6 x + y 2 − y + z 2 + 2 z − 23 4 = 0 Then, try to make the complete square term of the same variables. Then for that add and subtract 3 2 in the variable x terms, then ( 1 2 ) 2 in the variable y term and similarly 1 2 in z term. So, x 2 − 6 x + y 2 − y + z 2 + 2 z − 23 4 = 0 [ x 2 − 2 ⋅ x ⋅ 3 + 3 2 ] − 3 2 + [ y 2 − 2 ⋅ y ⋅ 1

11th Edition

ISBN: 9781337604789

Author: Larson

Publisher: Cengage

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Question

Chapter 11.2, Problem 46E

To determine

To calculate: The center and radius of sphere 4x2+4y2+4z2−24x−4y+8z−23=0 rewrite in standard form.

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Chapter 11.2, Problem 45E

Chapter 11.2, Problem 47E

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Chapter 11 Solutions

Bundle: Llf Multivariable Calculus

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The center and radius of sphere 4 x 2 + 4 y 2 + 4 z 2 − 24 x − 4 y + 8 z − 23 = 0 rewrite in standard form.

Solution Summary: The author explains how to calculate the center and radius of a sphere by rewriting the equation in standard form.

To calculate: The center and radius of sphere 4x2+4y2+4z2−24x−4y+8z−23=0 rewrite in standard form.

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Chapter 11 Solutions