JEE Main 2022MathematicsHyperbolaEasyMCQ

JEE Main 2022 — Hyperbola Question with Solution

JEE Main 2022 (26 Jul Shift 2)

Question

If the line x-1=0, is a directrix of the hyperbola kx2-y2=6, then the hyperbola passes through the point

Choose an option

Show full solutionCorrect option: C
Correct answer
C5,-2

Step-by-step explanation

Given equation of hyperbola is x26k-y26=1

Equation of directrix will be x=±ae,

Where e=1+b2a2=1+66k=1+k

i.e. k≥-1

 ⇒x=±6k1+k is the equation of directrix

i.e. ±6k1+k=1

∴   k1+k2=6⇒k2+k-6=0

⇒ k=2 as k=-3 is rejected

So equation of hyperbola will be H≡x23-y26=1

∴  5,-2 satisfy the given hyperbola

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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.