Say we've got a function such as $f(x)=x \cdot \sin(x)$ and we want to place a line of length $L$ on the graph that has its start and endpoints located on the line generated by $f(x)$. Assuming that we choose the starting point $(x_1, f(x_1))$, is there a way to analytically (not numerically) find the coordinate $(x_2, f(x_2))$ such that $\sqrt{(x_1 - x_2)^2 + (f(x_1) - f(x_2))^2} = L$?
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Note that given $P_1(x_1,y_1)$ there are at least two possibilities for $P_2(x_2,y_2)$ but because of the "oscillations" of $f(x)$ this number of possibilities for $P_2$ is not bounded and depends of lenght the line $L$ (sorry for bad English) – Piquito Nov 18 '21 at 13:51
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@Piquito yes, that's true – Dmitri Nesteruk Nov 18 '21 at 14:48