Edit: Here's a solution for the trigonometry in Python (credit to my wife, who pointed out the problem was an ellipse, not a circle):

    # FunkyEllipse.py
    
    import math
    
    n_dist=5000
    e_dist=2000
    s_dist=1500
    w_dist=1000
    
    distV=[n_dist,e_dist,s_dist,w_dist,n_dist]
    radix=0
    
    nverts=120              #!! Must be evenly divisible by 4!
    quad=nverts / 4
    
    step=(math.pi * 2) / nverts
    stepSin = math.sin(step);
    stepCos = math.cos(step);
    
    acc1   = 1.0            # Cos(90)
    acc2   = 0.0            # Sin(90)
    coords = []
    for i in range(0,nverts):
        if ((radix % 2) == 0):
            x = acc2 * distV[(radix+1)%4]
            y = acc1 * distV[radix%4]
        else:
            x = acc2 * distV[radix%4]
            y = acc1 * distV[(radix+1)%4]
    
        coords.append([x,y])
    
        if ((i % quad) == (quad - 1)):
            radix += 1
    
        temp = (acc1 * stepCos) - (acc2 * stepSin)
        acc2 = (acc2 * stepCos) + (acc1 * stepSin)
        acc1 = temp
    
    coords.append(coords[0])
    print str(coords)


Which generates a shape which looks like:
[![enter image description here][1]][1]

Incorporating the math in an arcpy script to copy a point featureclass to polygon is left as an exercise.

  


  [1]: https://i.sstatic.net/oEA5k.jpg