Combining existing approaches, we provide a uniform way to describe all hyperplanes which separate (properly, or strongly) a given pair of nonempty convex sets
K_1
K
1
and
K_2
K
2
in the
n
n
-dimensional Euclidean space. The method is based on considering
(n\! -\! 1)
(
n
−
1
)
-dimensional subspaces which bound the set
K_1 \!-\! K_2
K
1
−
K
2
and then using properties of the polar cone
(K_1 \!-\! K_2)^\circ
(
K
1
−
K
2
)
∘
. First, we characterize all separating hyperplanes with given normal vectors, and then those containing a given point. We also describe the union of all hyperplanes separating (properly separating) a given pair of convex sets.