# Problem about an ellipse distance between two distance in another view

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.

• Both $x_A$ and $x_B$ are located at first quadrant or $x_A = (1, 0)$ and $x_B$ is located at first quadrant. – 石原秀一 Jul 23 '19 at 3:18