I have been told that the directrix of a hyperbola is given as $$x = \pm\frac{a^2}{c}.$$
I cannot find any simple but convincing proof of this anywhere.
The hyperbola is of the form $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1.$$
Can anyone help with a proof of this?
Let assume that conjugate axis is parallel to y axis, hence the directrix equation is : x-T=0 , $\frac{(x_1-c)^2+y_1^2}{(x_1-T)^2}=e^2$, $a^2+b^2=c^2$ & c=ae, Solving we get T= $\frac{a^2}{c}$ As Hyperbola has two directrix other is negative of it