The planets in our solar systems have elliptical orbits because our sun has a directionality as well, it orbits Sirius, and the planets are dragged along. Likewise, the planets orbiting Sirius have elliptical orbits, and are dragged along as Sirius orbits our sun, causing them to have orbits as in the image below.

Sirius B is an exoplanet, and has an orbital period of 50 years, and an elliptical orbit, like all planets in our solar system have, the exact same type of orbit.

The orbital period of "Sirius B" has been measured to 50 years. From our sun, we are observing "Sirius B" as it is dragged along Sirius, which moves in the opposite direction our sun as the two stars orbit one another. The orbit appears to have a larger difference between aphelion and perihelion then it has, because we are observing it from an angle

Synapses

Bond, H. E., Schaefer, G. H., Gilliland, R. L., Holberg, J. B., Mason, B. D., Lindenblad, I. W., … Gudehus, D. (2017). The Sirius System and Its Astrophysical Puzzles: Hubble Space Telescope and Ground-based Astrometry. The Astrophysical Journal, 840(2), 70. https://doi.org/10.3847/1538-4357/aa6af8