tangent | A search engine for math expressions

I have created an SVG as shown in the below image.

SVG Path

Here, I require to give color to the path only to a certain point. It is to represent the progress of a user in his journey.

1. I searched for any SVG properties that could achieve this functionality like stroke-dashoffset, and stroke-dasharray. But, they didn't work.
2. I tried with stroke animations, but it didn't work.

Next, I thought of achieving this by drawing another path to the required point on the existing path and give stroke to that. This would solve my problem.

But, the problem I am facing is that if the required point is on the curved portion of the path shown in the image, I cannot draw the new path exactly overlapping the previous path.

I have drawn the previous curve using this

d="M 0 130L 820 130M 820 130C 1140 130 1140 466 820 466"

To draw the new path, I was able to draw only up to M 0 130L 820 130M 820 130C x1 y1 x2 y2 1049 350

I could not draw the curve exactly because I don't know how to get the control points x1, y1, x2, and y2. I am thinking of using ellipse equation, tangents and other mathematical stuff, but I don't know how feasible it would be in this case.

Is there any straight approach for giving stroke to the first path up to the required point?

If not, how can I get the control points?

hope you're all fine.

That's my first question, so I'm sorry if something's not right about it.

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Here's what is expected :

Here's the code :