The complex plane is equipped with a direct orthonormal coordinate system ($\mathrm{O}; \vec{u}, \vec{v}$).\\
We denote by $\mathscr{C}$ the set of points $M$ in the plane with affix $z$ such that $|z - 2| = 1$.

\begin{enumerate}
  \item Justify that $\mathscr{C}$ is a circle, and specify its center and radius.
  \item Let $a$ be a real number. We call $\mathscr{D}$ the line with equation $y = ax$. Determine the number of intersection points between $\mathscr{C}$ and $\mathscr{D}$ as a function of the values of the real number $a$.
\end{enumerate}