For the polar curve $r=a(1+cos\theta)$, I am trying to find the equations of the tangents perpendicular to the initial line by setting $\frac{dx}{d\theta}$ equal to zero. I am able to factorise a sine term out, so one of the solutions I get is that there is at theta=pi. Problem is that this is also a solution to tangents parallel to the initial line... On the curve, it seems to come in as a peak at this point. Now I am not sure whether it should be treated as tangents parallel or perpendicular to the initial line...
Thank you in advance!