The equation Ax^{2} + Bxy + Cy^{2} + 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 B
^{2}− 4AC = 0 - An ellipse if B
^{2}− 4AC < 0 - A hyperbola if B
^{2}− 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.