Conic sections

import sys
import numpy as np

def classify_conic(A, B, C, D, E, F):
    Q = np.array( ((A, B/2, D/2), (B/2, C, E/2), (D/2, E/2, F)) )
    Q = np.matrix(Q)
    Q33 = Q[:2,:2]

    detQ = np.linalg.det(Q)
    detQ33 = np.linalg.det(Q33)
    if detQ == 0:
        if detQ33 < 0:
            return 'two intersecting lines'
        if detQ33 == 0:
            return 'two parallel lines'
        return 'a single point'

    if detQ33 < 0:
        return 'a hyperbola'
    if detQ33 == 0:
        return 'a parabola'
    if A == C and B == 0:
        return 'a circle'
    return 'an ellipse'

A, B, C, D, E, F = [float(arg) for arg in sys.argv[1:]]
print(classify_conic(A, B, C, D, E, F))