Find the coordinates of the foci and the length of the latus rectum of the hyperbola (x2/9)-(y2/16)=1.

Question

Find the coordinates of the foci and the length of the latus rectum of the hyperbola (x2/9)-(y2/16)=1. (A) (0, ±2), (32/3) (B) (0, ±5), (32/3) (C) (±5, 0), (32/3) (D) (0, ±5), (3/32)

Tardigrade Admin · Accepted Answer

We have, a = 3, b = 4 and c=√a2+b2=√9+16=5 Therefore, the coordinates of the foci are (± 5,0). Also, length of latus rectum =(2b2/a)=(32/3)

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

$(0, \pm 2), \frac{32}{3}$

$(0, \pm 5), \frac{32}{3}$

$(\pm 5, 0), \frac{32}{3}$

$(0, \pm 5), \frac{3}{32}$

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

Q. Find the coordinates of the foci and the length of the latus rectum of the hyperbola 9x2​−16y2​=1.

(0,±2),332​

(0,±5),332​

(±5,0),332​

(0,±5),323​