What is the definition of axis?

Answer 1

There are two different definitions, depending on the context.

In coordinate (or analytical) geometry an axis is one of one or more numbered straight lines. If there are more than one line, usually they are orthogonal - that is, they meet at 90 degree angles.

The second definition of an axis is in the context of symmetry. Given any shape, an axis is a straight line such that the shape is symmetric about that line. The shape may have 2 or more dimensions.

These two concepts are related in the sense that the equation of the shape usually becomes much simpler if its axis of symmetry is made into one of the coordinate axes. However, mathematicians knew about axes of symmetry long before coordinate geometry was developed.