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Chapter 10: Q.30 (page 699)

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

r=41-cos胃

Short Answer

Expert verified

The rectangular equation isy2=8x+16

Step by step solution

01

Step 1. Given Information

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

r=41-cos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=41-cos胃r1-cos胃=4r-rcos胃=4r=4+rcos胃r2=4+rcos胃2

Plugging the values:

x2+y2=4+x2x2+y2=16+8x+x2y2=8x+16

03

Step 3. Conclusion

The rectangular equation of the given polar equation isy2=8x+16

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