Let H be hyperbola, whose foci are (1 pm √{2}, 0) and eccentricity is √{2} . Then length of its

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10-2. Parabola, Ellipse, Hyperbola

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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

$2$

B

$3$

C

$\frac{5}{2}$

D

$\frac{3}{2}$

(JEE MAIN-2023)

Solution

$2 ae =|(1+\sqrt{2})-(1+\sqrt{2})|=2 \sqrt{2}$

$ae =\sqrt{2}$

$a =1$

$\Rightarrow b =1 \quad \because e =\sqrt{2} \Rightarrow \text { Hyperbola is rectangular }$

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

Standard 11

Mathematics

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