   Chapter 11.2, Problem 42E

Chapter
Section
Textbook Problem

# Finding the Equation of a SphereIn Exercises 43–46, complete the square to write the equation of the sphere in standard form. Find the center and radius. x 2 + y 2 + z 2 + 9 x − 2 y + 10 z + 19 = 0

To determine

To calculate: The center and radius of sphere x2+y2+z2+9x2y+10z+19=0 rewrite in standard form.

Explanation

Given:

The equation is x2+y2+z2+9x2y+10z+19=0.

Formula used:

The equation of sphere is (xl)2+(ym)2+(zm)2=r2 where (l,m,n) are the center points and r is the radius.

The formula from algebra is:

(ab)2=a22ab+b2(a+b)2=a2+2ab+b2

Calculation:

Consider the equation x2+y2+z2+9x2y+10z+19=0.

Then, group the same variable terms.

x2+y2+z2+9x2y+10z+19=0x2+9x+y22y+z2+10z+19=0

Then, try to make the complete square term of the same variables.

Then for that add and subtract (92)2 in the variable x terms, then 12 in the variable y term and similarly 52 in z term.

So,

x2+2x92+(92)2(92)2+y22y1+1212+z2+2z5+5252+

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