A *conic*, or *conic section*, is one of the two-dimensional shapes you can get by cutting a slice through a cone: an *ellipse* (including a circle), a *parabola* or a *hyperbola*. These shapes are also the graphs of quadratic equations in two variables.

The general Cartesian equation for these curves is \[ax^2+2hxy+by^2+2fx+2gy+c=0.\] The type of curve can be determined by computing \(h^2-ab\):

\(h^{2}-ab < 0\) | ellipse (or circle) |

\(h^{2}-ab = 0\) | parabola |

\(h^{2}-ab > 0\) | hyperbola |

There are also degenerate possibilities if the slice passes through the vertex of the cone; in terms of the equation, some choices of the parameters \(a\), \(b\), … will give these or equations with no real solutions.