JEE Main 2023 — Hyperbola Question with Solution
From: JEE Main 2023 (Online) 6th April Evening Shift
Question
Let the eccentricity of an ellipse is reciprocal to that of the hyperbola . If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is ___________.
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Show full solutionCorrect answer: 2
Correct answer
2
Step-by-step explanation
Equation of hyperbola is
Here,
Eccentricity of rectangular hyperbola is
Eccentricity of ellipse is
Since, ellipse intersects the hyperbola at right angles
Ellipse and the hyperbola are confocal
Foci of hyperbola
Foci of ellipse,
Length of the latus rectum
Square of length of the latus rectum
Here,
Eccentricity of rectangular hyperbola is
Eccentricity of ellipse is
Since, ellipse intersects the hyperbola at right angles
Ellipse and the hyperbola are confocal
Foci of hyperbola
Foci of ellipse,
Length of the latus rectum
Square of length of the latus rectum
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This is a previous-year question from JEE Main 2023, covering the Hyperbola chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.