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I have just solved the problem the distance between two points on the circumference of an ellipse following the outer curve after I read the following article.

Is it possible to find the distance between two points on the circumference of an ellipse following the outer curve?

Then I want to solve this problem in another view.

Please watch the example below which link of a question of the owner I have pasted above.

example ←here

This ellipse's equation is $\frac{x^2}{2^2} + \frac{y^2}{1^2} = 1$ (Just what original question has mentioned).

So my question is, suppose we know arc-length between two points $x_A$ and $x_B$ and we know Coordinate of $x_A$, how to calculate coordinate of $x_B$?If this solution is impossible, we can assume that $x_A$ = (0, 1).In this case, the equation has very strong Symmetry, so I think we can solve the problem.

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I think we can calculate the coordinates of the other point. If you are trying to solve the strength using integrals with a single variable then you have upper and lower bounds. Since you know the limit of one bound you can solve the other bound.

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  • $\begingroup$ Both $x_A$ and $x_B$ are located at first quadrant or $x_A = (1, 0)$ and $x_B$ is located at first quadrant. $\endgroup$ – 石原秀一 Jul 23 '19 at 3:18
  • $\begingroup$ So what do you mean? Is there a formula to solve this problem? $\endgroup$ – 石原秀一 Jul 23 '19 at 10:37

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