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.