Question

For the hyperbola whose transverse and conjugate axes are respectively 6 and 4 and whose centre is at the origin

• A. foci are $(\pm \sqrt{13},0)$
• B. latus rectum $=2\sqrt{7}$
• C. $e=\sqrt{13}/4$
• D. none of these

Answer 1

The correct option is A foci are $(\pm \sqrt{13},0)$

$2a=6$, $2b=4$

$\Rightarrow a=3$, $b=2$

$e=\sqrt{1+\frac{b^2}{a^2}}=\sqrt{1+\frac{4}{9}}=\sqrt{\frac{13}{9}}$

focii $=\pm ae,0$

$=\pm 3\times \frac{\sqrt{13}}{3},0$

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