Input Data

P := RandomGoodPoly(30):
N := 150:
a := [0.4, 0.1, 0.2, 0.3]:

EllipseProperties(P, alpha = a, scaling = "norm"):
AnimateConvergence(P, N, alpha = a, scaling = "norm");

Output Data

Under norm rescaling, the limiting ellipse will have normal form equation:
26.02 x^2 + -33.87 xy + 26.02 y^2 = 1
which has:
semi-major axis length = 0.3317
semi-minor axis length = 0.1526
eccentricity = 0.88795
with the semi-major axis tilted at an angle of 135.00 degrees counter-clockwise from the x-axis.