Calculating the exact length of an SVG Arc in Python?

I want to be able to calculate the exact length of an SVG Arc. I can do all the manipulations rather easily. But, I am unsure of whether there is a solution at all or the exact implementation of the solution.

Here's the exact solution for the circumference of the ellipse. Using popular libraries is fine. I fully grasp that there are no easy solution as they will all require hypergeometric functions to be exact.

from scipy import pi, sqrt
from scipy.special import hyp2f1

def exact(a, b):
    t = ((a - b) / (a + b)) ** 2
    return pi * (a + b) * hyp2f1(-0.5, -0.5, 1, t)

a = 2.667950e9
b = 6.782819e8
print(exact(a, b))

My idea is to have this as opt-in code if you happen to have scipy installed it'll use the exact super-fancy solution, else it'll fall back to the weaker approximation code (progressively smaller line segments until error is small). The problem is the math level here is above me. And I don't know if there's some ways to specify a start and stop point for that.

Most of the approximation solutions are for ellipses, but I only want the arc. There may also be a solution unknown to me, for calculating the length of an arc on an ellipse but since the start and end position can be anywhere. It doesn't seem to be instantly viable to say a sweep angle is 15% of the total possible angle therefore it's 15% of the ellipse circumference.

A more effective less fancy arc approximation might also be nice. There are progressively better ellipse approximations but I can't go from ellipse circumference to arc length, so those are currently not helpful.

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