  The purpose of this article is twofold. The first aim is to prove that if
there exist a sequence $\{\varphi_j\}\subset \mathrm{Aut}(\Omega)$ and $a\in
\Omega$ such that $\lim_{j\to\infty}\varphi_j(a)=\xi_0$ and
$\lim_{j\to\infty}\sigma_\Omega(\varphi_j(a))=1$, where $\xi_0$ is a linearly
convex boundary point of finite type, then $\xi_0$ must be strongly
pseudoconvex. Then, the second aim is to investigate the boundary behaviour of
the squeezing function of a general ellipsoid.
