• The discriminant of a non-degenerate conic curve (NDCC) in the real Cartesian plane determined by a non-degenerate quadratic equation of the form
  • $Ax^2 + Bxy +Cy^2 +Dx +Ey + F = 0$
    is given by
    $ \Delta = B^2 -4AC$.

  • I will present a simple proof of the classification of the conic (ellipse, parabola, or hyperbola) by the discriminant.


  • The proof is based on understanding homogeneous coordinates in real projective algebraic geometry and the related 3 dimensional coordinate geometry.