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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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Finding the Equation of a Sphere In Exercises 7–10, find the standard equation of the sphere with the given characteristics.

Endpoints of a diameter: (3, −4, −1), (1, 0, −5)

To determine

To calculate: The standard equation of sphere with endpoints of diameter at (3,4,1) and (1,0,5).

Explanation

Given information:

The provided sphere with endpoints of diameter at (3,4,1) and (1,0,5).

Formula used:

The midpoint of the line segment joining the two points (x1,y1,z1) and (x2,y2,z2) is

Midpoints= (x1+x22,x1+x22,x1+x22)

The distance between two points (x1,y1,z1) and (x2,y2,z2) is

d[(x1,y1,z1) to (x2,y2,z2)]=(x1x2)2+(y1y2)2+(z1z2)2

The standard equation of sphere with center at (a,b,c) radius R is

(xa)2+(yb)2+(zc)2=R2

Calculation:

Consider the endpoints of the diameter,

(3,4,1) and (1,0,5),

Now the apply midpoint formula to find the midpoint of the line segment joining the two points (3,4,1) and (1,0,5) is

Midpoints= (3+12,4+02,152)=(42,42

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