Math Homework. Do It Faster, Learn It Better.


For each focus of any conic section, there is a fixed line on the convex side, called the directrix, perpendicular to the axis of symmetry .  For each point on the graph, its distance from the focus is directly proportional to its distance from the corresponding directrix.  The proportionality constant is called the eccentricity , written e .

eccentricity ( e ) = distance from point to focus distance from point to directrix

The value of eccentricity determines the type of conic.

      If e = 0 , the conic is a circle .

      If 0 < e < 1 , the conic is an ellipse .  (The closer e is to zero, the more circular is the ellipse.)

      If e = 1 , the conic is a parabola .

If e > 1 , the conic is a hyperbola .