How to fit a curve in a picture with an equation?

For a curve taken from a picture, is there any method to fit it with an equation if it appears to be some standard curve?

For example, in the following picture, the curve looks like an ellipse or a circle or something else of a conic section. How can I fit the shape with a proper equation using Mathematica? Furthermore, is it possible to assess two different fittings with a criterion (e.g. error)? Thank you in advance.

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