### 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 $\frac{2 b^{2}}{a}=2$