   Chapter 11, Problem 12RE

Chapter
Section
Textbook Problem

# Finding the Equation of a SphereIn Exercises 11 and 12, complete the square to write the equation of the sphere in the standard form. Find the center and radius. x 2 + y 2 + z 2 − 10 x + 6 y − 4 z + 34 = 0

To determine

To calculate: For given equation of the sphere x2+y2+z210x+6y4z+34=0. Find theequation of the sphere in standard form.

Explanation

Given: The equation of the sphere is:

x2+y2+z210x+6y4z+34=0

Formula used: The distance formula is used to find the standard equation of a sphere of radius r, centered at (x0,y0,z0). If (x,y,z) is an arbitrary point on the sphere, then the equation of the sphere is:

r=(xx0)2+(yy0)2+(zz0)2

Calculation:

Now, Use factorization in the equation and group the terms

x2+y2+z210x+6y4z+34=0

(x210x)+(

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