The physical properties of T Pyx as measured by MUSE I. The geometrical distribution of the ejecta and the distance to the remnant

T Pyx is one of the most enigmatic recurrent novae, and it has been proposed as a potential Galactic type-Ia supernova progenitor. Using spatially-resolved data obtained with MUSE, we characterized the geometrical distribution of the material expelled in previous outbursts surrounding the white dwarf progenitor. We used a 3D model for the ejecta to determine the geometric distribution of the extended remnant. We have also calculated the nebular parallax distance ($d = 3.55 \pm 0.77$ kpc) based on the measured velocity and spatial shift of the 2011 bipolar ejecta. These findings confirm previous results, including data from the GAIA mission. The remnant of T Pyx can be described by a two-component model, consisting of a tilted ring at $i = 63.7$ deg, relative to its normal vector and by fast bipolar ejecta perpendicular to the plane of the equatorial ring. We find an upper limit for the bipolar outflow ejected mass in 2011 of the bipolar outflow of $M_{ej,b} < (3.0 \pm 1.0) \times 10^{-6}$ M$_{\odot}$, which is lower than previous estimates given in the literature. However, only a detailed physical study of the equatorial component could provide an accurate estimate of the total ejecta of the last outburst, a fundamental step to understand if T Pyx will end its life as a type-Ia supernova.