  In this expository paper we review on the existence problem of
Einstein-Maxwell K\"ahler metrics, and make several remarks. Firstly, we
consider a slightly more general set-up than Einstein-Maxwell K\"ahler metrics,
and give extensions of volume minimization principle, the notion of toric
K-stability and other related results to the general set-up. Secondly, we
consider the toric case when the manifold is the one point blow-up of the
complex project plane and the K\"ahler class $\Omega$ is chosen so that the
area of the exceptional curve is sufficiently close to the area of the rational
curve of self-intersection number 1. We observe by numerical analysis that
there should be a Killing vector field $K$ which gives a toric K-stable pair
$(\Omega, K)$ in the sense of Apostolov-Maschler.
