Let $\mathcal{C}$ be a graph given by $x=by^a$ where $b\in \mathbb{R}$ is just a constant and $a \in \mathbb{Q}_+^*$

Question

Let $\mathcal{C}$ be a graph given by $$x=by^a$$ where $b\in \mathbb{R}$ is just a constant and $a \in \mathbb{Q}_+^*$.

Under the assumptions above, Is it possible to say that the graph $\mathcal{C}$ is smooth and tangent to the $y-$axis to order $[a]$ (where $[a]$ is greatest integer less than or equal to $a$)?