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Hyperbola question

2024 · 27 Jan · Shift 2 · Q38

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JEE Main
Mathematics
Hyperbola
2024 · 27 Jan · Shift 2 · Q38

Hyperbola question

2024 · 27 Jan · Shift 2 · Q38

JEE MainMathematicsHyperbolaMCQ+4 / −1

Let

e_1

be the eccentricity of the hyperbola

\frac{x^2}{16}-\frac{y^2}{9}=1

and

e_2

be the eccentricity of the ellipse

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \mathrm{a} \gt \mathrm{b}

, which passes through the foci of the hyperbola. If

\mathrm{e}_1 \mathrm{e}_2=1

, then the length of the chord of the ellipse parallel to the

x

-axis and passing through

(0,2)

is :

A
$\frac{8 \sqrt{5}}{3}$
B
$3 \sqrt{5}$
C
$4 \sqrt{5}$
D
$\frac{10 \sqrt{5}}{3}$

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