JEE Main 2016MathematicsStraight LinesHardMCQ

JEE Main 2016 — Straight Lines Question with Solution

JEE Main 2016 (09 Apr Online)

Question

If a variable line drawn through the intersection of the lines x3+y4=1 and x4+y3=1 , meets the coordinate axes at A and B, A ≠B,then the locus of the midpoint of AB is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A7xy=6x+y

Step-by-step explanation

L1 :4x+3y-12=0

L2:3x+4y-12=0

L1+λL2=0

⇒4x+3y-12+λ3x+4y-12=0

⇒x4+3λ+y3+4λ-121+λ=0

Point A121+λ4+3λ, 0

Point B0,121+λ3+4λ

Mid point ⇒h=61+λ4+3λ .......i

k=61+λ3+4λ .......ii

Eliminate λ from equations i and ii then

6h+k= 7hk

Hence, locus is

6x+y= 7xy

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About this question

This is a previous-year question from JEE Main 2016, covering the Straight Lines 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.