Curve Fitting Methods

What kind of curve-fitting method would be best to find an equation (if there is one) for this curve?

• It seems an rotated hyperbola, in Wolfram Mathematica \[Theta] = \[Pi]/8; Graphics[{Line@Table[{Cos[\[Theta]] Cosh[t] - 0.5 Sin[\[Theta]] Sinh[t],Sin[\[Theta]] Cosh[t] + 0.5 Cos[\[Theta]] Sinh[t]}, {t, -3, 3, 0.01}]}] Commented Apr 12, 2023 at 19:00
• I though about that, but since the scales of the x and y axis are different from one another in the picture, wouldn't it be slightly off from a hyperbola? Commented Apr 12, 2023 at 19:08
• I suppose the stretch in one direction would only affect the eccentricity of the hyperbola, but don't know for sure. Should have the original data to make some test, to better understand Commented Apr 12, 2023 at 19:11
• Yes, I do have the actual numbers. Also, I guess I could take the coordinates to be (constant*y) and that would make the picture consistent. Commented Apr 12, 2023 at 19:14
• Of course, you could always split the curve into two functions, then you can use pretty much any common curve fitting method you'd like for functions (with a boundary condition that they meet). This would be (imo) the easiest, but also most rudimentary. Commented Apr 12, 2023 at 22:32