The polar equation of a conic section becomes much easier to work with if a focus is placed at the origin. A directrix (either vertical or horizontal) is then placed so that it does not go through the focus.[br][br]This interactive figure dynamically illustrates the polar equation of such a conic with [color=#ff00ff][b]focus [i]F [/i][/b][/color]and given [color=#980000][b]directrix[/b][/color]. The eccentricity, [i]e[/i], is defined to be the ratio of the [color=#1e84cc][b]distance from the focus to any point on this conic[/b][/color] to the [b][color=#38761d]distance from this point to its directrix[/color][/b]. You can move[color=#9900ff][b] point [i]P[/i][/b][/color] anywhere on the graph of this conic. [br][br][b]Note:[/b] [br][list][*]If 0 < [i]e[/i] < 1, the conic is an ellipse.[br][/*][*]If [i]e[/i] = 1, the conic is a parabola.[br][/*][*]If [i]e[/i] > 1, the conic is a hyperbola. [br][/*][/list]

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