Let the foci of a hyperbola H coincide with the foci of the ellip… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 9 April, Shift 2Conic Sections (Parabola, Ellipse, Hyperbola)

Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E$ : $\frac{(x-1)^2}{100} + \frac{(y-1)^2}{75} = 1$ , and the eccentricity of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$ . If the length of the transverse axis of $H$ is $\alpha$ and the length of its conjugate axis is $\beta$ , then $3\alpha^2 + 2\beta^2$ is equal to:

A
$242$
B
$225$
C
$237$
D
$205$

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