Hyperbola Question 4
Question 4 - 31 January - Shift 2
Let $H$ be the hyperbola, whose foci are $(1 \pm \sqrt{ } 2,0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is
(1) 2
(2) 3
(3) $\frac{5}{2}$
(4) $\frac{3}{2}$
Show Answer
Answer: (1)
Solution:
Formula: Eccentricity of hyperbola (9.9), Length of latus rectum (9.4), Foci (9.2),
$2 ae=|(1+\sqrt{2})-(1-\sqrt{2})|=2 \sqrt{2}$
ae $=\sqrt{2}$
$a=1$
$\Rightarrow b=1 $
$ \because e=\sqrt{2} \Rightarrow$ Hyperbola is rectangular
$\therefore$ The length of its latus rectum is $\frac{2 b^{2}}{a}=2$
