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

Standard equation of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ with foci $S(a e, 0) and S^{\prime}(-a e, 0)$ Given equation is $4 x^2-9 y^2=1$ or, $\quad \frac{x^2}{\left(\frac{1}{4}\right)}$-\frac{y^2}{\left(\frac{1}{9}\right)}=1$Here,$\quad a^2=\frac{1}{4}, \quad b^2=\frac{1}{9}$From hyperbola properties, or,$$\begin{aligned} b^2 & =a^2 e^2-a^2 \\ a^2 e^2 & =b^2+a^2 \\ & =\frac{1}{9}+\frac{1}{4}=\frac{13}{36} \end{aligned}$$\text{ or, } \quad a e= \pm \frac{\sqrt{13}}{6}$ Hence, foci : $\left( \pm \frac{\sqrt{13}}{6}, 0\right)