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