The axis of a parabola is the line which divides the parabola into two symmetrically equal parts. The following figure shows this:

The axis divides the parabola symmetrically 
The mirror image of each point on the parabola on one side of the axis lies on the other side of the axis. If you draw a line perpendicular to the axis meeting the parabola at two points then those two points are mirror images of each other.
The axis of a parabola is defined as the line perpendicular to the
directrix and passing through its
focus. This is shown in the following figure:

Axis of a parabola is perpendicular to the directrix and passes through its focus 
The axis of a parabola can also be defined as the line passing through the
vertex and perpendicular to the directrix.
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