JEE Main 2020MathematicsStraight LinesEasyNumerical

JEE Main 2020 — Straight Lines Question with Solution

JEE Main 2020 (05 Sep Shift 1)

Question

If the line, 2 x-y+3=0 is at a distance 15 and 25 from the lines 4x-2y+α=0 and 6x-3y+β=0 respectively, then the sum of all possible values of α and β is ____________.

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Show full solutionCorrect answer: 30
Correct answer
30

Step-by-step explanation

2 x-y+3=0……(i)

4x-2y+α=0  ⇒  2x-y+α2=0……(ii)6x-3y+β=0  ⇒  2x-y+β3=0……(iii)

d1=α2-322+12=15⇒|α-6|=2

⇒  α-6=2,-2⇒  α=8,4

d2=β3-322+12=25  ⇒  |β-9|=6

⇒  β-9=6,-6  ⇒  β=15,3

Sum of all values of α and β=30.

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About this question

This is a previous-year question from JEE Main 2020, 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.