# 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
$e$
.

$\text{eccentricity}\left(e\right)=\frac{\text{distancefrompointtofocus}}{\text{distancefrompointtodirectrix}}$

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 .