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Hyperbola question

2022 · 24 Jun · Shift 2 · Q44

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JEE Main
Mathematics
Hyperbola
2022 · 24 Jun · Shift 2 · Q44

Hyperbola question

2022 · 24 Jun · Shift 2 · Q44

JEE MainMathematicsHyperbolaNumerical+4 / −1

Let the hyperbola

H:{{{x^2}} \over {{a^2}}} - {y^2} = 1

and the ellipse

E:3{x^2} + 4{y^2} = 12

be such that the length of latus rectum of H is equal to the length of latus rectum of E. If

{e_H}

and

{e_E}

are the eccentricities of H and E respectively, then the value of

12\left( {e_H^2 + e_E^2} \right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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