JEE Main 2022MathematicsHyperbolaEasyNumerical

JEE Main 2022 — Hyperbola Question with Solution

JEE Main 2022 (25 Jun Shift 2)

Question

Let the eccentricity of the hyperbola x2a2-y2b2=1 be 54. If the equation of the normal at the point 85,125 on the hyperbola is 85x+βy=λ, then λ-β is equal to _____.

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Show full solutionCorrect answer: 85
Correct answer
85

Step-by-step explanation

Using the formula of eccentricity we get,

e2=1+b2a2=2516⇒b2a2=916     ...1

A85,125 satisfies x2a2-y2 b2=1

⇒645a2-14425 b2=1     ...2

Solving 1 & 2 b=65a=85

Normal at A is 5a2x8+5 b2y12=a2+b2

Comparing it 85x+βy=λ

Gives λ=100,β=15

So, λ-β=85

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About this question

This is a previous-year question from JEE Main 2022, 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.