How do i find the arc length of a curve at a certain point (x,y)

A point has zero length! You must have a finite interval to get the length.

If you know y = f(x), then you can find the arc-length from, say x=a to x=b from the following integral:

$$\int_a^b\sqrt{1+(\frac{dy}{dx})^2}dx$$

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You will need to use Arc length parameterisation, here's a short video on it If you're not that familiar with it; https://www.youtube.com/watch?v=SbSMASTymfw

Mmm I have to think about that one Alan :/

I'll try to set some time aside to play with it