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

Euclidean and chemical distances in ellipses percolation