Limacon Curves
Key Questions

Limaçon curves look like circles. They have various types depending on the values in their equations.
In the image below, for example, the types of limaçon curves are: dimpled, cardioid, and looped (respectively).

Answer:
It's easiest to watch a video of this.
Here's one I made a while backExplanation:
I think the video will help you out a lot.

Answer:
#r^2=a^2 cos 2theta# .
The graph is the fallen eight, looking like the symbol#oo# ...Explanation:
For the double loop of
#r^2=a^2 cos 2theta, cos 2theta >=0# .So, the range for
#theta in [0, 2pi]# excludes#(pi/4, (3pi)/4)# and#((5pi)/4, (7pi)/4)# , Here,#cos 2theta < 0# ...