If the Foci of a Hyperbola Are... |JEE Main 2024 | Hyperbola

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JEE MAIN 2024

31-01-2024 S1

Question

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

Select the correct option:

A

$7 \sqrt{\frac{2}{5}}-\frac{8}{3}$

B

$14 \sqrt{\frac{2}{5}}-\frac{4}{3}$

C

$14 \sqrt{\frac{2}{5}}-\frac{16}{3}$

D

$7 \sqrt{\frac{2}{5}}+\frac{8}{3}$

✓ Correct! Well done.

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