Question

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

• A. $\left(\pm \sqrt{13,}0\right)$
• B. $\left(\pm \sqrt{\frac{13}{6},}0\right)$
• C. $\left(0,\pm \sqrt{\frac{13}{6}}\right)$
• D. None of these

Answer 1

Answer: (B)

The given equation of hyperbola can be re-written as,
$\frac{x^2}{{\left(\frac{1}{2}\right)}^2}-\frac{y^2}{{\left(\frac{1}{3}\right)}^2}=1$
So, the hyperbola has $x$-axis as the transverse axis, with $a=\frac{1}{2}$
and $b=\frac{1}{3}$
And, $e=\sqrt{1+\frac{b^2}{a^2}}$
$=\sqrt{1+\frac{4}{9}}=\frac{\sqrt{13}}{3}$
$\therefore$ Focii $=(\pm ae,0)=\left(\pm \frac{\sqrt{13}}{6},0\right)$