**The discriminant of a non-degenerate conic curve (NDCC) in the real Cartesian plane determined by a non-degenerate quadratic equation of the form**- 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.