JEE Main 2021MathematicsStraight LinesEasyMCQ

JEE Main 2021 — Straight Lines Question with Solution

JEE Main 2021 (26 Aug Shift 1)

Question

Let ABC be a triangle with A(-3,1) and ∠ACB=θ,0<θ<π2. If the equation of the median through B is 2x+y-3=0 and the equation of angle bisector of C is 7x-4y-1=0, then tanθ is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B43

Step-by-step explanation

Let, x-coordinate of the point C is α, So coordinate of the point   Cα,7α-14  ∵(C lies on 7x-4y-1=0)

 Hence, mid point of AC is mα-32,7α+38

As, point m lies on the line 2x+y-3=0, Substituting, we get α=3.

So. C(3,5)

Hence, slope of AC is 23 and slope of 7x-4y-1=0 is74

∴tanθ2=74-231+74×23=12

⇒tanθ=2·121-14=43⇒tanθ=43

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About this question

This is a previous-year question from JEE Main 2021, 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.