I aim to solve the following problem:
I managed to prove that $\sec\theta>0$ ,however, I have had little success in graphing it and showing it is a conchoid of Nicomedes. The locus of points (source MEI) is given by
I do not understand why the graph is symmetric around $b$ as I think that $r=\pm b + a\sec\theta$ meaning that the graph should be the same but shifted by b, but this is wrong according to MEI and the markscheme. If anybody could shine some light into how to graph the polar curve in $(i)$ I would greatly appreciate it.
Edit Here is the mark scheme for the first part of the question 