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)

$2ae=|(1+\sqrt{2})-(1+\sqrt{2})|=2\sqrt{2}$
$ae=\sqrt{2}$
$a=1$
$\Rightarrow b=1$
$\because e=\sqrt{2}$
$\Rightarrow$ Hyperbola is rectangular
$\Rightarrow L\cdot R=\frac{2b^2}{a}=2$