Additively transtable conic sections with respect to fixed coefficients

Abstract

The arithmetic mean has several important properties. One of them preserves the result of the arithmetic mean. That is, if one value increases and another decreases, the result of the arithmetic mean is the same. This property is called transfer stability, transtability for short. We can see its reach in several mathematical theories. The most common use is with aggregation functions. This article aims to show another use of this property, specifically in the geometry of conic sections. We have outlined how the transtability of a conic section works. The main idea was to find a common property for conic sections connected by transtability. We found that these conics have the same common intersection and the set of all centers forms a conic.