Question

What is meant by the eccentricity of a hyperbola?

Answer 1

Eccentricity of a hyperbola:

Eccentricity is the ratio of the distance of point on the hyperbola from the focus and the directrix and is denoted by $\left(e\right)$.

The eccentricity of the hyperbola is greater than $1$, i.e. $e>1$.

The general equation of a hyperbola is:

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

And the eccentricity formula is:

$e=\frac{c}{a}$, where $c=\sqrt{a^2+b^2}$

For any hyperbola, $a$ and $b$ are the length of semi-transverse axis and semi-conjugate axis.

Thus, eccentricity is the ratio of the distance of point on the hyperbola from the focus and the directrix and is denoted by $\left(e\right)$.