Mathematics - Hyperbola Question with Solution | TestHub

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