This activity is also a vehicle for the introduction of the Geometer's Sketchpad , though no prior experience with the Sketchpad is assumed. The Definition We begin by introducing the focus - directrix definition of the conic section. The directrix is a line. The focus is a point, usually chosen so that it does not lie on the directrix. Let's begin with a focal point at the origin of our coordinate system and a vertical line k units from the origin, as shown in Figure 1.
All ellipses have eccentricity less than one.
For purposes of discussion, we need to draw the auxiliary line segment PB and label some existing line segments, angles, and points. This we do in Figure 3. Let r and q represent the segment FP and the angle BFP, respectively. The Geometer's Sketchpad is one of the really fine pieces of software that seems to have the right mix of technology and pedagogy. Demonstration software is also available for trial use.