We have been given graph of a limacon curve. We are asked to choose the equation that represents the given Limacon.
We can see that our given equation represents a cardiod. The equation of a vertical cardiod is in form [tex]r=a\pm a\cdot \text{sin}(\theta)[/tex] and equation of a horizontal cardiod is [tex]r=a\pm a\cdot \text{cos}(\theta)[/tex].
We can see that our given graph is a vertical cardiod, so its equation will be in form [tex]r=a\pm a\cdot \text{sin}(\theta)[/tex] .
The positive sign gives an upside-down cardiod and negative sign orients the cardiod upright.
Since our given graph is upright, so we will have a negative sign between 'a'.
Therefore, the equation [tex]r=2-2\cdot \text{sin}(\theta)[/tex] represents the given graph and option 'd' is the correct choice.
