  In this paper, we generalize the Minkowski distance by defining a new
distance function in n-dimensional space, and we show that this function
determines also a metric family as the Minkowski distance. Then, we consider
three special cases of this family, which generalize the taxicab, Euclidean and
maximum metrics respectively, and finally we determine circles of them with
their some properties in the real plane. While we determine some properties of
circles of the generalized Minkowski distance, we also discover a new
definition for the ellipse.
