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Eccentricity

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 $e$ .

$\text{eccentricity}\left(e\right)=\frac{\text{distance from point to focus}}{\text{distance from point to directrix}}$

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 .