  We use the EAGLE cosmological simulations to perform a comprehensive and
systematic analysis of the $z=0.1$ Fundamental Plane (FP), the tight relation
between galaxy size, mass and velocity dispersion. We first measure the total
mass and velocity dispersion (including both random and rotational motions)
within the effective radius to show that simulated galaxies obey a total mass
FP that is very close to the virial relation ($<10\%$ deviation), indicating
that the effects of non-homology are weak. When we instead use the stellar
mass, we find a strong deviation from the virial plane, which is driven by
variations in the dark matter content. The dark matter fraction is a smooth
function of the size and stellar mass, and thereby sets the coefficients of the
stellar mass FP without substantially increasing the scatter. Hence, both
star-forming and quiescent galaxies obey the same FP, with equally low scatter
(0.02 dex). We employ simulations with a variable stellar initial mass function
(IMF) to show that IMF variations have a modest additional effect on this FP.
Moreover, when we use luminosity-weighted mock observations of the size and
spatially-integrated velocity dispersion, the inferred FP changes only
slightly. However, the scatter increases significantly, due to the
luminosity-weighting and line-of-sight projection of the velocity dispersions,
and measurement uncertainties on the half-light radii. Importantly, we find
significant differences between the simulated FP and observations, which likely
reflects a systematic difference in the stellar mass distributions. Therefore,
we suggest the stellar mass FP offers a simple test for cosmological
simulations, requiring minimal post-processing of simulation data.
