Final answer:
An ellipse's foci are normally along the major axis, but if they coincide on the minor axis, the shape would be a circle with zero eccentricity as the distance between foci would be zero. The orientation of the axes is important in calculations of orbital movement as in Kepler's laws, and in physics for calculating objects' moments of inertia.
Step-by-step explanation:
The concept of an ellipse involves understanding its axes. The ellipse has two axes: the major axis and the minor axis. By definition, the major axis is the longest diameter and the minor axis is the shortest. The foci of an ellipse are two specific points located along the major axis. When the foci coincide at the same point along the minor axis, the ellipse becomes a circle, because an ellipse is defined by two points (the foci), and when they are at the same point, there is no longer any difference in distances to boundary points of the figure.
According to Kepler's Second Law, which relates to orbital motion, the focus on the semi-major axis is the parent body, like the sun in our solar system, and the other focus lies along the same line. This orientation underscores the importance of the major axis in determining an object's orbit. In physics, when calculating the moment of inertia, which is a measure of an object's resistance to changes in its rotation, the axis of rotation is significant. For a thin rod (which can be treated as a string of masses along a line), the moment of inertia is calculated about an axis—often the center of mass to simplify the calculation. The parallel-axis theorem simplifies this process further for axes parallel to that through the center of mass.
In summary, what would be a circle with a focus on the minor axis, is actually an ellipse with its foci located at that one central point. The moment of inertia calculations for physical objects like rods take into account the axis about which rotation occurs and is significantly simplified by the use of the parallel-axis theorem.