The equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 represents either a (non–degenerate) conic or a degenerate conic. If it is a conic, then it is
- A parabola if B2 − 4AC = 0
- An ellipse if B2 − 4AC < 0
- A hyperbola if B2 − 4AC > 0
Classification of conics with respect to eccentricity
If e < 1, then the conic is an ellipse.
If e = 1, then the conic is a parabola.
If e > 1, then the conic is a hyperbola.