Parametric Curve(s)

$$$ \forall\alpha\in\{0,2\pi\}\quad\; 0\leqslant\;k_{a}\;\leqslant2.8\quad\;$$$
$$$ \left \{ \begin{array}{r c l} \theta(\alpha)& = &\alpha \\ r(\alpha)& = &0.1\times\left (\cos{\alpha}-k_{a}\right ) \end{array}\right .$$$