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Chapter 10: Q 35 (page 777)

Describe the graphs of the equations and provide alternative equations in the specified coordinate systems

Change蚁=2 to the rectangular and cylindrical systems

Short Answer

Expert verified

The equation in rectangular coordinates isx2+y2+z2=4

The equaion in cylindrical coordinates isr2+z2=4

Step by step solution

01

Step 1:Given information

The given expression is蚁=2

02

Step 2:Simplification

To convert 蚁=2into rectangular coordinates

In rectangular coordinates we have

x2+y2+z2=蚁2

Since 蚁=2

鈬�x2+y2+z2=4

So, it represents a sphere with center at origin

03

Step 3:Simplification

To convert 蚁=2into cylindrical coordinates we have

x=rcos胃,y=rsin胃,z=z

substituting in the above equation

width="198" height="22" role="math">鈬�r2cos2胃+r2sin2胃+z2=4

width="195" height="22" role="math">鈬�r2cos2胃+sin2胃+z2=4

鈬�r2+z2=4

Therefore,the equaion in cylindrical coordinates isr2+z2=4

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