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Chapter 10: Q.31 (page 699)

In Problems 30 and 31, convert each polar equation to a rectangular equation.

r=84+8cos胃

Short Answer

Expert verified

The rectangular equation is3x2-y2-8x+4=0

Step by step solution

01

Step 1. Given Information

Given to convert the below polar equation to a rectangular equation.

r=84+8cos胃

02

Step 2. Calculation

A polar equation is converted to rectangular equation by using the substitutions r2=x2+y2,rcos胃=x,rsin胃=y

Rewriting the given equation to get the above terms:

r=84+8cos胃r4+8cos胃=84r+8rcos胃=8r+2rcos胃=2r=2-2rcos胃r2=2-2rcos胃2

Plugging the values:

x2+y2=2-2x2x2+y2=4-8x+4x23x2-y2-8x+4=0

03

Step 3. Conclusion

The rectangular equation of the given polar equation is3x2-y2-8x+4=0

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