  The ellipses model is a continuum percolation process in which ellipses with
random orientation and eccentricity are placed in the plane according to a
Poisson point process. A parameter $\alpha$ controls the tail distribution of
the major axis' distribution and we focus on the regime $\alpha \in (1,2)$ for
which there exists a unique infinite cluster of ellipses and this cluster
fulfills the so called highway property. We prove that the distance within this
infinite cluster behaves asymptotically like the (unrestricted) Euclidean
distance in the plane. We also show that the chemical distance between points
$x$ and $y$ behaves roughly as $c \log\log |x-y|$.
