This applet shows a geometric construction of the conics based on their eccentricity. We use the following definition: Let [math]d[/math] be a line (directrix) and [math]F[/math] be a fixed point (focus) in the plane. A conic section is the locus of all points [math]L[/math] in the plane such that the ratio of the distances from [math]L[/math] to [math]F[/math] and from [math]L[/math] to [math]d [/math] is a constant. This constant [math]e[/math] is the [i]eccentricity[/i]. [br][list][br][*]Drag the slider to see how the conic section changes based on the eccenticity.[br][/list][br]If [math]0<e<1[/math] , then the conic is an [i]ellipse[/i], if [math]e=1[/math], the conic is a [i]parabola[/i], and if [math]e>1[/math], it is a [i]hyperbola[/i].[br][list][br][*]Click the “Show Constructions” to see the details of the construction steps. The loci are based on the point [math]G[/math] moving along the ray [math]BG[/math], where [math]BG/BH = BD/BC = e[/math]. [br][*]Drag point G and trace the loci.[br][/list]