Parametric Curve(s)

$$$ \forall\alpha\in\{0,2\pi\}\quad0\leqslant\;k_{a}\;\leqslant0.227$$$
$$$ \left \{ \begin{array}{r c l} \theta(\alpha)& = &0.2\times\tan{(0.1+k_{a}\cdot\alpha)} \\ r(\alpha)& = &0.2\times\cos{(\alpha)}+\frac{t}{3} \end{array}\right .$$$