Question

Identify the type of polar graph for the equation: r = 3-5cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex limacon eRose Curve fCircle gLemniscate

Answer 1

Given the equation:

`r=3-5\cos \theta`

Let's identify the type of polar graph for the equation.

To identify the type of polar graph, use the formula below to get the Cartesian form:

`(x^2_{}+y^2)=r(\cos \theta,\sin \theta)`

Thus, we have:

`(x^2+y^2)=3\sqrt[]{x^2+y^2}-5x`

We have the graph of the equation below:

We can see the graph forms a Limacon with an inner loop.

Therefore, the type of polar graph for the given equation is a limacon with inner loop.

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