JEE Main 2023MathematicsStraight LinesHardMCQ

JEE Main 2023 — Straight Lines Question with Solution

JEE Main 2023 (01 Feb Shift 1)

Question

If the orthocentre of the triangle, whose vertices are 1,2,2,3 and 3,1 is α,β, then the quadratic equation whose roots are α+4β and 4α+β, is

Choose an option

Show full solutionCorrect option: D
Correct answer
Dx2-20x+99=0

Step-by-step explanation

We have,

Here mBH×mAC=-1

⇒β-3α-21-2=-1

⇒β-3=2α-4

⇒β=2α-1        ....(1)

mAH×mBC=-1

⇒β-2α-1-2=-1

⇒2β-4=α-1

Using (1), we can write:

⇒2(2α-1)-4=α-1

⇒22α-1=α+3

⇒3α=5

α=53, β=73⇒H53,73

α+4β=53+283=333=11

β+4α=73+203=273=9

Required equation is

x2-20x+99=0

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About this question

This is a previous-year question from JEE Main 2023, 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.