So there is an oval hole in a metal casting. It’s supposed to be an elliptical hole. Is it ????? How can we find out ?????

A good start would be to find the line which would be the major axis if it was elliptical. This turns out to be an engineering problem, not a mathematical one (I cannot see a way!). If the oval curve has an axis of symmetry then the method below will find it:

Firstly, get a computer picture of the oval.

Take two circles, of different radii, and push them along until each one touches the oval in two places.

The line joining the two centers will be the axis of symmetry if there is one (this can be shown mathematically).

The equation of an ellipse uses the lengths of the major and minor axes. Do it !

The closeness to elliptic can be assessed in various ways. Think of one.

next…..finding the focus of a parabolic shape