The foci of hyperbola 4 x^2-9 y^2-1=0 are

Given, Hyperbola $=4 x^2-9 y^2-1=0$$\begin{aligned} & \Rightarrow \frac{x^2}{\left(\frac{1}{4}\right)}-\frac{y^2}{\left(\frac{1}{9}\right)}=1 \\ & \Rightarrow \frac{x^2}{\frac{1}{2}^2}-\frac{y^2}{\frac{1}{3}^2}=1 \end{aligned}$We know that. if hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. then Eccentricity: $e=\sqrt{1+\frac{b^2}{a^2}}\begin{aligned} & \text{and focus } \equiv( \pm \text{be}, 0)=\left( \pm \frac{1}{2} \times \frac{\sqrt{1 / 3}}{3}, 0\right)=\left( \pm \frac{\sqrt{13}}{6}, 0\right) \end{aligned}$$$