Question

Consider the limaçon with equation r = 3 4cos(θ). how does the quotient of a and b relate to the existence of an inner loop?

Answer 1

If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.

Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.

Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.

formula of polar graph is similar to r= a+ b cos (θ).

Case 1. If a<b or b/a>1

then the curve is a limacon with inner loop.

Case 2. If a>b or b/a<1

Then the limacon does not have an inner loop.

Here given that $r=3+4cos$ (θ)

It is observed that , a<b or b/a>1

Therefore the curve is limacon with an inner loop.

Hence because b/a>1 the curve is a limacon with an inner loop.

Learn more about limacon at brainly.com/question/14322218

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