Question

Find the directrix of a hyperbola?

Answer 1

Solve for the directrix of a hyperbola

Directrix of a hyperbola is a straight line that is used in generating a curve. It can also be defined as the line from which the hyperbola curves move away from. This line is perpendicular to the axis of symmetry.

General hyperbola equation is given by:

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

The focus of hyperbola is given by $(\pm c,0)$ and $c^2=a^2+b^2$ where $(a,0)$ and $(-a,0)$ are the two vertices.

Let $e$ is the eccentricity of hyperbola then the directrix is the line which is parallel to $y$ axis and is given by

$x=\pm \frac{a}{e}$

Hence the directrix of hyperbola is $\pm \frac{a}{e}$