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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 a trace of a Sphere In Exercises 13 and 14, find the equation of the xy-trace of the sphere. Then sketch the xy-trace of the sphere.

( x 1 ) 2 + ( y + 3 ) 2 + ( z 6 ) 2 = 72

To determine

To calculate: The equation of the xy-trace of sphere (x1)2+(y+3)2+(z6)2=72 and sketch the xy-trace of sphere.

Explanation

Given information:

The provided equation of sphere (x1)2+(y+3)2+(z6)2=72.

Formula used:

The traced of any surface represents intersection of coordinate’s plane with surface.

Calculation:

Consider the equation of sphere

(x1)2+(y+3)2+(z6)2=72

Substitute, 0 for z in above equation,

(x1)2+(y+3)2+(6)2=72

Simplify the equation,

(x1)2+(y+3)2+(6)2=72(x1)2+(y+3)2=36(x1)2+(y+3)2=62

The equation of xy-trace of sphere (x1)2+(y+3)2+(z6)2=72 is a circle (x1)2+(y+3)2=62 of radius 6.

Hence, the equation of xy-trace of sphere (x1)2+(y+3)2+(z6)2=72 is circle (x1)2+(y+3)2=62 with center (1,3) and circle of radius 6

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