don't know the syntax for having a list in the θ range, so each curve is drawn separately.

https://www.desmos.com/calculator/glxs2rxapv ]]>

https://www.desmos.com/calculator/mfegywuuxb ]]>

https://www.desmos.com/calculator/u63qbamtxs ]]>

And I found the hidden parabola! (Hint: Click on the graph and observe the pattern made by the minima.)

]]>https://www.desmos.com/calculator/pfkf7r0j1m ]]>

This is what i got, i had to google how to start but once i got my r value, all i had to do was play around with my a values until it resembled the graph given. ]]>