What is meant by the eccentricity of a hyperbola?

1 Answer
Aug 30, 2015

The eccentricity of a hyperbola is the ratio of the distance from any point on the graph to (a) the focus and (b) the directrix.


A hyperbola is a curve where the distances of any point from a fixed point (the focus) and a fixed straight line (the directrix) are always in the same ratio.


This ratio is called the eccentricity #e#.

The equation for a hyperbola is:

#x^2/a^2 − y^2/b^2 = 1#


The formula for eccentricity #e# is

#e = sqrt(a^2+b^2)/a#

The eccentricity measures the degree of opening of the branches of the hyperbola.

The greater the eccentricity, the more open the arms of the hyperbola.