Question

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

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

Answer 1

Answer: (B)

$(\pm \frac{\sqrt{13}}{6},0)$

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 $=(\pm ae,0)=(\pm \frac{\sqrt{13}}{6},0)$

Hence, B is correct.