QJEEM23Ma11f6: JEE Main 2023 Mathematics - Class 11 JEEM23Ma11f6 Solution: Let be the hyperbola, whose foci are and eccentricity is . Then …

Question

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Let

\mathrm{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 :

Accepted Answer

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

\Rightarrow

\mathrm{ae}=\sqrt{2}

\Rightarrow

\mathrm{a}=1

\Rightarrow \mathrm{b}=1 \because \mathrm{e}=\sqrt{2} \Rightarrow

Hyperbola is rectangular

\Rightarrow \mathrm{L} . \mathrm{R}=\frac{2 \mathrm{~b}^{2}}{\mathrm{a}}=2

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