Program in Numpy (Python) that takes in five points from a graph and returns the coefficients for the function of that graph

I want to create a program in Numpy (Python) that takes in five points from a graph and returns the coefficients for the function of that graph. Mathematically it would be like this:

PS: I know this question is a lot so even if you can't completely answer it I understand but I would appreciate a tip or at least the name of a NumPy library that could help me do this and I'll research it.

From that, I just want to know how to implement it into NumPy. Please help!

I know I have to subtract the polynomials so I have this:

def find_conic():
  # define the polynomials
  # p(x) = 5(x**2) + (-2)x +5
  px = (5,-2,5)
  
  # q(x) = 2(x**2) + (-5)x +2
  qx = (2,-5,2)
  
  # subtract the polynomials
  rx = np.polynomial.polynomial.polysub(px,qx)
  
  # print the resultant polynomial
  print(rx)

find_conic()

I would then have to substitute the subtracted equation into each other to get the equation for a for example.

source https://stackoverflow.com/questions/70160614/program-in-numpy-python-that-takes-in-five-points-from-a-graph-and-returns-the

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