Equations of directrices of $4{\mathrm{x}}^2-9{\mathrm{y}}^2=36$ is

$$\begin{gathered} \mathrm{Given} \mathrm{hyperbola} \frac{{\mathrm{x}}^2}{9}-\frac{{\mathrm{y}}^2}{4}=1 \\ \mathrm{when} {\mathrm{a}}^2=9, {\mathrm{b}}^2=4 \\ \mathrm{e}=\sqrt{\frac{9+4}{9}}=\frac{\sqrt{13}}{3} \\ \mathrm{Now} \mathrm{equations} \mathrm{of} \mathrm{directrices} \mathrm{are} \mathrm{x}=\pm \frac{\mathrm{a}}{\mathrm{e}} \\ =\pm \frac{3}{{\displaystyle \frac{\sqrt{13}}{3}}} \\ \Rightarrow x =\pm \frac{9}{\sqrt{13}} \\ \Rightarrow \sqrt{13}\mathrm{x}=\pm 9 \end{gathered}$$