Question 447854
{{{Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0}}}
The conic sections described by this equation can be classified with the discriminant {{{B^2  - 4AC}}}.

If the conic is non-degenerate, then:
--> if  {{{B^2  - 4AC}}} < 0, the equation represents an ellipse;
**if A = C and B = 0, the equation represents a circle, which is a special case of an ellipse;
--> if  {{{B^2  - 4AC}}} = 0, the equation represents a parabola;
--> if  {{{B^2  - 4AC}}} > 0, the equation represents a hyperbola;
**if we also have A + C = 0, the equation represents a rectangular hyperbola.