Let E: (x²)/(a²) + (y²)/(b²) = 1, a > b and H: (x²)/(A²) - (y²)/(B²) = 1. Let the distance between the foci of E and the foci of H be 2√(3). If a - A = 2, and the ratio of the eccentricities of E and H is 1/3, then the sum of the lengths of their latus rectums is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q45

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

Let

\mathbf{E}: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, a > b

and

\mathbf{H}: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1

. Let the distance between the foci of

\mathbf{E}

and the foci of

\mathbf{H}

2\sqrt{3}

. If

a - A = 2

, and the ratio of the eccentricities of

\mathbf{E}

and

\mathbf{H}

\frac{1}{3}

, then the sum of the lengths of their latus rectums is equal to:

JEE Main 2025 Coordinate Geometry Question with Solution (January Unspecified (session-level dataset), Q45) | JEE Arc