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Hyperbola question

2024 · 31 Jan · Shift 1 · Q50

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JEE Main
Mathematics
Hyperbola
2024 · 31 Jan · Shift 1 · Q50

Hyperbola question

2024 · 31 Jan · Shift 1 · Q50

JEE MainMathematicsHyperbolaMCQ+4 / −1

If the foci of a hyperbola are same as that of the ellipse

\frac{x^2}{9}+\frac{y^2}{25}=1

and the eccentricity of the hyperbola is

\frac{15}{8}

times the eccentricity of the ellipse, then the smaller focal distance of the point

\left(\sqrt{2}, \frac{14}{3} \sqrt{\frac{2}{5}}\right)

on the hyperbola, is equal to

A
$14 \sqrt{\frac{2}{5}}-\frac{4}{3}$
B
$7 \sqrt{\frac{2}{5}}+\frac{8}{3}$
C
$7 \sqrt{\frac{2}{5}}-\frac{8}{3}$
D
$14 \sqrt{\frac{2}{5}}-\frac{16}{3}$

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