Aims. ESO 243-49 HLX-1, otherwise known as HLX-1, is an intermediate mass black hole (IMBH) candidate located 8 (3.7 Kpc) from the centre of the edge-on S0 galaxy ESO 243-49. How the black hole came to be associated with this galaxy, and the nature of the environment in which it resides, are still unclear. Using multi-wavelength observations we investigate the nature of the medium surrounding HLX-1, search for evidence of past mergers with ESO 243-49 and constrain parameters of the galaxy. Methods. We reduce and analyse integral field unit observations of ESO 243-49 that were taken with the MUSE instrument on the VLT. Using complementary multi-wavelength data, including X-Shooter, HST, Swift, Chandra and ATCA data, we further examine the vicinity of HLX-1. We additionally examine the nature of the host galaxy and estimate the mass of the central supermassive black hole (SMBH) in ESO 243-49. Results. No evidence for a recent minor-merger that could result in the presence of the IMBH is discerned, but the data are compatible with a scenario in which minor mergers may have occurred in the history of ESO 243-49. The MUSE data reveal a rapidly rotating disc in the centre of the galaxy, around the SMBH. The mass of the SMBH at the centre of ESO 243-49 is estimated to be 0.5-23 $times$ 10$^7$ M$_odot$. Studying the spectra of HLX-1, that were taken in the low/hard state, we determine H$_alpha$ flux variability to be at least a factor 6, compared to observations taken during the high/soft state. This H$_alpha$ flux variability over one year indicates that the line originates close to the IMBH, excluding the possibility that the line emanates from a surrounding nebula or a star cluster. The large variability associated with the X-ray states of HLX-1 confirms that the H$_alpha$ line is associated with the object and therefore validates the distance to HLX-1.
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