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Problem

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Textbook Expert
Textbook ExpertVerified Tutor
18 Nov 2021

Given information

Given that the family of curves .

Step-by-step explanation

Step 1.

The given equation of the curve is  . Now we have ti checkthe changes that occur in the curve equation when  increases and  changes: 

Consider: 

Put  : 

Using the equation, the curve has one lobe.  

Put:  

Using the given polar equation, the curve has two lobes. 

Consider, 

 , then the curves are congruent. 

The lobes analysis depends on the number of lobes n: 

If  is even then the curve has big and  small lobes. 

If is odd then the curve has inner and outer lobes. 

 

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