## Related questions with answers

Question

For a concert, a circular stage is constructed and placed in the center so fans can completely surround the musicians. To record the sound of the crowd, two directional microphones are placed next to each other on the stage, one facing due east and the other facing due west. The patterns of the microphones can be represented by the polar equations $r=2.5+2.5 \cos \theta$ and $r=-2.5-2.5 \cos \theta.$ Identify the type of curve given by each polar equation.

Solution

VerifiedStep 1

1 of 2Note that the given polar equations are in the form $r=a+b\cos(\theta)$ which creates limacon. More specifically, since $a=b$, these polar equations create $\boxed{\color{#4257b2}\text{cardioids}}$.

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