   Chapter 7.1, Problem 44E ### 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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# Finding the Center and Radius of a Sphere In Exercises 39-44, find the center and radius of the sphere. See Example 6. 4 x 2 + 4 y 2 + 4 z 2 − 8 x − 16 y + 11 = 0

To determine

To calculate: The centre and radius of sphere whose equation is 4x2+4y2+4z28x+16y+11=0.

Explanation

Given Information:

The equation of sphere, 4x2+4y2+4z28x+16y+11=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:

The equation of sphere can be written as,

4x2+4y2+4z28x+16y+11=04(x2+y2+z22x+4y+114)=0x2+y2+z22x+4y+114=0

Convert the provided equation into the square by grouping the similar variable. So, the above equation can be written as:

(x22x)+(y2+4y)+z2+114=0(x22x)+(y2+4y)+z2=114

To complete the square, add the half of square of each linear term of the equation

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