Asymmetric separation of convex sets

Based on various types of asymmetric hyperplane separation of a given pair of convex sets $K_1$ and $K_2$ in the $n$-dimensional Euclidean space, we derive a uniform description of existing types of separation. Our argument uses properties of the polar cone $(K_1 - K_2)^\circ$. Also, we consider asymmetric separation of convex cones with a common apex.