Let's explore the polar equations as following:
I recommend to observe the each animation which I linked with Graphing Calulator 3.2 files.
Case 1: The variable a is changing from -2 to 2.
To see the animation, please click here.
Case 2: The variable b is changing from -2 to 2.
To see the animation, please click here.
Case 3: The variable c is changing from -5 to 5. The following graphs are the cases when c=-5, -4, -3, -2, -1, 0.
Case 4: The variable d is changing from -5 to 5.
To see the animation, please click here.