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Chapter 9: Q. 68 (page 622)

In space, the collection of all points that are

the same distance from some fixed point is called a sphere.

See the illustration. The constant distance is called the

radius, and the fixed point is the center of the sphere. Show

that the equation of a sphere with center at x0,y0andz0and

radius r is

(x-x0)2+(y-y0)2+(z-z0)2=r2

Short Answer

Expert verified

The equation of sphere comes out to be

(x-x0)2+(y-y0)2+(z-z0)2=r2

Step by step solution

01

Step 1. Given

Center (x0,y0,z0)and radius r.

02

Step 2. Calculation

Assume a point (x,y,z)on the sphere. now since the center of the sphere is (x0,y0,z0)therefore by applying distance formulae get:

role="math" localid="1646887500864" d(P0,P)=(x-x0)2+(y-y0)2+(z-z0)2(x-x0)2+(y-y0)2+(z-z0)2=r2

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