jee-main 2022 Q68

jee-main · India · session2_25jul_shift2 Conic sections Eccentricity or Asymptote Computation

Let the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{7} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{\alpha} = \frac{1}{25}$ coincide. Then the length of the latus rectum of the hyperbola is:
(1) $\frac{32}{9}$
(2) $\frac{18}{5}$
(3) $\frac{27}{4}$
(4) $\frac{27}{10}$

Let the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{7} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{\alpha} = \frac{1}{25}$ coincide. Then the length of the latus rectum of the hyperbola is:\\
(1) $\frac{32}{9}$\\
(2) $\frac{18}{5}$\\
(3) $\frac{27}{4}$\\
(4) $\frac{27}{10}$

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