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JEE Main 20253 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
3 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2025 · 3 April · Evening Shift · Mathematics · Straight Lines

Consider the lines x(3 λ+1)+y(7 λ+2)=17 λ+5 , λ being a parameter,...

Consider the lines x(3λ+1)+y(7λ+2)=17λ+5\mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5, λ\lambda being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of LL from the point (3,6)(3,6) is dd, then the value of d2d^2 is

Options

  1. A2020
  2. B3030
  3. C1010
  4. D1515

Correct answer

A. 2020

Step-by-step solution

<br/>x(3λ+1)+y(7λ+2)=17λ+5(x+2y−5)+λ(3x+7y−17)=0<br/>\begin{aligned}<br/>& \mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5 \\ & (\mathrm{x}+2 \mathrm{y}-5)+\lambda(3 \mathrm{x}+7 \mathrm{y}-17)=0<br/>\end{aligned}
intersection of family of lines
P(1,2)\mathrm{P}(1,2)
Let Q(3,6)\mathrm{Q}(3,6)
<br/>d=PQ=22+42=20 d2=20<br/>\begin{aligned}<br/>& \mathrm{d}=\mathrm{PQ}=\sqrt{2^2+4^2}=\sqrt{20} \\ & \mathrm{~d}^2=20<br/>\end{aligned}
option (1)
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