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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 + 6 x 8 y + 2 z 10 = 0 .

To determine

To calculate: The centre and radius of sphere whose equation is x2+y2+z2+6x8y+2z10=0.

Explanation

Given Information:

The equation of sphere, x2+y2+z2+6x8y+2z10=0.

Formula used:

The standard equation of a sphere with centre at (h,k,j) and radius r is,

(xh)2+(yk)2+(zj)2=r2

Calculation:

Consider equation of sphere,

x2+y2+z2+6x8y+2z10=0

The standard equation of sphere in square form. So, the provided equation of sphere converts into the square by grouping the similar variable. So, the above equation can be written as,

x2+y2+z2+6x8y+2z10=0(x2+6x)+(y28y)+(z2+2z)=10

To complete the square, add the half of square of each linear term of the equation. So, to complete the square of (x2+6x), add [12(6)]2=9 to both sides

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