This applet shows a geometric construction of the conics based on their eccentricity. We use the following definition: Let be a line (directrix) and be a fixed point (focus) in the plane. A conic section is the locus of all points in the plane such that the ratio of the distances from to and from to is a constant. This constant is the eccentricity.

Drag the slider to see how the conic section changes based on the eccenticity.

If , then the conic is an ellipse, if , the conic is a parabola, and if , it is a hyperbola.

Click the “Show Constructions” to see the details of the construction steps. The loci are based on the point moving along the ray , where .