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Eccentricity

For eachfocusof any conic section, there is a fixed line on the convex side, called the directrix, perpendicular to theaxis of symmetry. For each point on the graph, its distance from the focus isdirectly proportionalto its distance from the corresponding directrix. Theproportionality constantis called theeccentricity, 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 acircle.

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

If$e=1$, the conic is aparabola.

If$e>1$, the conic is ahyperbola.