The following applet was designed to serve as a reference with respect to the standard form of the equation of a parabola (one main type of conic section.) [br][br][color=#c51414]Recall that "p" represents the displacement of the focus (F) from V.[/color] Since displacement can be negative at times, [color=#c51414]p[/color] is negative whenever [br][br]a) the focus lies below the parabola's vertex (when the parabola's axis of symmetry is vertical) or [br]b) the focus lies to the left of the parabola's vertex (when the parabola's axis of symmetry is horizontal).

Complete this activity once for any parabola with a vertical axis of symmetry.[br]Then repeat this activity once for any parabola with a horizontal axis of symmetry. [br][br]1) Plot a point on the parabola. [br]2) Measure the distance from this point plotted to the focus.[br]3) Measure the distance from this point plotted to the directrix. [br]4) Drag this point along the parabola now. What do you notice? [br]5) How does the distance from the vertex to the focus (of ANY parabola) compare with the distance from the vertex to the directrix?