JEE Main 2021MathematicsHyperbolaHardNumerical

JEE Main 2021 — Hyperbola Question with Solution

JEE Main 2021 (18 Mar Shift 1)

Question

A square ABCD has all its vertices on the curve x2y2=1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is

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Show full solutionCorrect answer: 80
Correct answer
80

Step-by-step explanation

xy=1, -1

t1+t22·1t1-1t22=1

⇒t22-t1=24t1t2

Product of slope =-1

1t12×-1t22=-1⇒t1t2=1

⇒t1t22=1⇒t1t2=1

⇒t12+t22=42+4=25

⇒t12=2+5⇒1t12=5-2

AB2=t1-t22+1t1+1t22

=2t12+1t12=45⇒ Area 2=80 sq. unit

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About this question

This is a previous-year question from JEE Main 2021, 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.