So I am trying to figure out if there is a formula/method for determining whether a given arc is part of an ellipse, or a circle given a chord length (Cl) and height (H).
Now the first arc comes from a unit circle.
The second, visually, at least, is obviously an arc portion of an ellipse.
The third though, is a bit more tricky... It actually still is part of an ellipse, but is a bit more difficult to visualize.
Now, intuitively at least, it seems to me that in the case of the circle, the angle of any portion of that arc should always be constant (?)-- Or, at least, the radius will always be constant for any point along the arc.
The second case could be identified if the radius of any point on the line varies (above ? below ?) the constant that one would find in the case of a circle.
But the third case, I am not so sure...
Further, I am kind of wondering whether or not there is a 'minimum chord length' needed to satisfy said conditions. Again, at least intuitively, it seems if the arc is 'too small' it may be too hard to tell (?)
I say 'applied' in this case because I don't have the formulae for said arcs-- Also, presume arc length (Al) is at least first unknown.
I am working from the impression of drawn arcs, so it would be possible for me to find the points, but I'd have to grid out and measure all the points.
Any thoughts would be greatly appreciated.