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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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Find the equation of the sphere that has the points (-2, 5, 7) and (4, 1, -3) as endpoints of a diameter.

To determine

To calculate: The standard equation of sphere that has points (2,5,7) and (4,1,3) as endpoints of a diameter.

Explanation

Given Information:

The endpoints of the diameter, (2,5,7) and (4,1,3).

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:

Consider the endpoints of the diameter, (2,5,7) and (4,1,3).

Since, the midpoint of the diameter of a sphere is the centre of sphere. So, by the use of midpoint formula,

Midpoint=(x1+x22,y1+y22,z1+z22)=(2+42,5+12,7+(3)2)=(1,3,2)

Since, the distance between the centre and circumference point of the sphere is the radius of the sphere

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