The [i]parabola[/i] is the [i]locus[/i] of points in that plane that are equidistant from a line, called [i]directrix[/i] and a fixed point, called [i]focus.[/i][br][br]Another way to view the graph of a parabola is by constructing its [i]envelope[/i], that is the set of all the tangent lines at any point of it.[br][br]In the following app you can:[br][list][*]set the position of the directrix by moving the two diamond points that define it[/*][*]set the position of the focus by dragging point [math]F[/math] [/*][*]start or pause the animation using the button on the bottom left, or move the green point along the directrix to animate the construction manually[/*][*]delete the trace of the envelope, using the button on top right [/*][/list][br]The point of intersection of the [i]perpendicular bisector [/i]of the segment that joins the moveable point to the focus with the perpendicular line to the directrix is equidistant from the focus and the directrix (why?). [br]When the point moves along the directrix, the perpendicular bisectors define the [i][color=#0000ff]envelope [/color][/i]of the [color=#1155cc][i]parabola[/i][/color].