JEE Main 2023MathematicsHyperbolaEasyMCQ

JEE Main 2023 — Hyperbola Question with Solution

JEE Main 2023 (31 Jan Shift 2)

Question

Let H be the hyperbola, whose foci are 1±2,0 and eccentricity is 2. Then the length of its latus rectum is:

Choose an option

Show full solutionCorrect option: C
Correct answer
C2

Step-by-step explanation

Given the foci points of a hyperbola are 1±2,0

So, S1+2,0,S'1-2,0

SS'=2ae=(1+2)-(1-2)

⇒2ae=22

⇒2×a×2=22, given e=2

⇒a=1

Since b2=a2(e2-1)

⇒b2=1(2-1)=1

So, the latus rectum of a hyperbola is given by,

L.R. =2b2a

L.R. =2

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About this question

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.