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.)
Recall that "p" represents the displacement of the focus (F) from V. Since displacement can be negative at times, p is negative whenever
a) the focus lies below the parabola's vertex (when the parabola's axis of symmetry is vertical) or
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.
Then repeat this activity once for any parabola with a horizontal axis of symmetry.
1) Plot a point on the parabola.
2) Measure the distance from this point plotted to the focus.
3) Measure the distance from this point plotted to the directrix.
4) Drag this point along the parabola now. What do you notice?
5) How does the distance from the vertex to the focus (of ANY parabola) compare with the distance from the vertex to the directrix?