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

The foci of hyperbola $4 x^2-9 y^2-1=0$ are
  1. $( \pm \sqrt{13}, 0)$
  2. $\left( \pm \frac{\sqrt{13}}{6}, 0\right)$
  3. $\left(0, \pm \frac{\sqrt{3}}{6}\right)$
  4. None of these

Solution

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: $e=\sqrt{1+\frac{b^2}{a^2}}$ $\begin{aligned} & \text {and focus } \equiv( \pm \text{be}, 0)=\left( \pm \frac{1}{2} \times \frac{\sqrt{1 / 3}}{3}, 0\right)=\left( \pm \frac{\sqrt{13}}{6}, 0\right) \end{aligned}$

Asked in: BITSAT 2024 (Memory Based Paper 3)

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