A [i]hyperbola [/i]is the set of points in a plane whose distances from two fixed points, called foci, have a constant difference. As you slide the slider, this definition is illustrated. (This feature is only available if the "Foci on [i]x[/i]-axis" checkbox is selected.) [color=#9900ff]The value of this constant difference is the distance between the hyperbola's vertices. [/color] You can drag [color=#980000][b]point [/b][i][b]P[/b] [/i][/color]anywhere on this hyperbola to see the illustration.[br][br]This interactive figure displays the graph of a hyperbola having center at the origin and [b][color=#ff00ff]foci [/color][/b] [math]F_1[/math] and [math]F_2[/math] . Here, [color=#1e84cc][i]a [/i]= the distance between the hyperbola's center and a vertex[/color], [color=#ff7700][i]c[/i] is the distance between the center and a focus[/color], and [math]b=\sqrt{c^2-a^2}[/math].

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]