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A Gallery of Conic Sections

The equation of each conic section is a second-degree polynomial function of two variables, and can be written in the form   $a_1x^2+a_2xy+a_3y^2+a_4x+a_5y+a_6=0$.   One property common to each of these curves is that it will intersect any given line at most 2 times. Non-degenerate quadratic plane curves are often called conic sections, since each can be obtained by slicing a double-napped cone.

Each of the graphs on this page is a quadratic plane curve, displayed in the window   $[-5,5]\times[-5,5]$.