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Hyperbola question

2022 · 27 Jul · Shift 1 · Q41

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JEE Main
Mathematics
Hyperbola
2022 · 27 Jul · Shift 1 · Q41

Hyperbola question

2022 · 27 Jul · Shift 1 · Q41

JEE MainMathematicsHyperbolaNumerical+4 / −1

An ellipse

E: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

passes through the vertices of the hyperbola

H: \frac{x^{2}}{49}-\frac{y^{2}}{64}=-1

. Let the major and minor axes of the ellipse

E

coincide with the transverse and conjugate axes of the hyperbola

H

, respectively. Let the product of the eccentricities of

E

and

H

be

\frac{1}{2}

. If

l

is the length of the latus rectum of the ellipse

E

, then the value of

113 l

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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