Question

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 _____

• A. 3
• B. $\frac{5}{2}$
• C. 2
• D. $\frac{3}{2}$

Answer 1

Answer: (C)

$ 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
$ \Rightarrow L \cdot R =\frac{2 b ^2}{ a }=2$