   Chapter 11.2, Problem 39E

Chapter
Section
Textbook Problem

# Finding the Equation of a Sphere In Exercises 37–42, find the standard equation of the sphere with the given characteristics. ( 2 , 1 , 3 ) , ( 1 , 3 , − 1 )

To determine

To calculate: The standard equation of sphere when the endpoints of the diameter (2,0,0),(0,6,0).

Explanation

Given:

The endpoints of the diameter (2,0,0),(0,6,0).

Formula used:

The general equation of sphere with center (a,b,c) and radius r is:

(xa)2+(yb)2+(zc)2=r2

Centre of line with end co-ordinate (x,y,z) and (a,b,c) is:

x+a2,y+b2,z+c2

Length of a line with end co-ordinate (x,y,z) and (a,b,c) is:

L=(xa)2+(yb)2+(zc)2

Calculation:

The endpoints of the diameter (2,0,0),(0,6,0).

Since, center of line with end co-ordinate (x,y,z) and (a,b,c) is:

x+a2,y+b2,z+c2

So,

x=2+02=22=1

y=0+62=62=3

z=0+02=02=0

So, the center of the sphere is (1,3,0)

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