Question

Find the coordinates of the foci and the length of the latus rectum of the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{16}=1.$

• A. $\left(0, \pm2\right), \frac{32}{3}$
• B. $\left(0, \pm5\right), \frac{32}{3}$
• C. $\left(\pm5, 0\right), \frac{32}{3}$
• D. $\left(0, \pm5\right), \frac{3}{32}$

Answer 1

Answer: (C)

We have, $a = 3$, $b = 4$ and
$c=\sqrt{a^{2}+b^{2}}=\sqrt{9+16}=5$
Therefore, the coordinates of the foci are $\left(\pm 5,0\right)$.
Also, length of latus rectum $=\frac{2b^{2}}{a}=\frac{32}{3}$