Question

What is meant by the eccentricity of a hyperbola?

Answer 1

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.

Explanation:

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.