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JEE Main 3-April-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 3-April-2025 Paper - Shift 24 Marks
MCQ
Consider the lines $x(3 \lambda+1)+y(7 \lambda+2)=17 \lambda+5$, $\lambda$ being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of $L$ from the point $(3,6)$ is $d$, then the value of $d^{2}$ is
  • A
    20
  • B
    30
  • C
    10
  • D
    15
✓

Answer

A. 20
$\mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5$
$(x+2 y-5)+\lambda(3 x+7 y-17)=0$
intersection of family of lines
$\mathrm{P}(1,2)$
Let $\mathrm{Q}(3,6)$
$d=P Q=\sqrt{2^{2}+4^{2}}=\sqrt{20}$
$\mathrm{d}^{2}=20$

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