This applet allows quick explorations of the general form of conic sections. [b] A x² + B x y + C y² + D x + E y + F = 0[/b] If [b]B² - 4A C < 0[/b], 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]B² - 4A C = 0[/b], the equation represents a parabola. If [b]B² - 4A C > 0[/b], the equation represents a hyperbola. (If we also have A + C = 0, the equation represents a rectangular hyperbola.) [b]B² - 4A C[/b] is called the [b]discriminant[/b] of the general formula for conic sections (although is looks the same as the discriminant of the quadratic equation, it is used differently and the coefficients are not the same).
References: [url=http://en.wikipedia.org/wiki/Conic_section]Conic Sectio[/url] and [url=http://en.wikipedia.org/wiki/File:Table_of_Conics,_Cyclopaedia,_volume_1,_p_304,_1728.jpg]an old textbook[/url] page; Inspiration site: [url=http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/conics.html]Mathlet-Conics[/url]