JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Straight Lines

Consider the lines

x (3 λ + 1) + y (7 λ + 2) = 17 λ + 5

λ

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}

(A)20✓ Correct
(B)30
(C)10
(D)15

Answer: (A)

Solution

The family is

(x + 2 y - 5) + λ (3 x + 7 y - 17) = 0

, concurrent at

P

where

x + 2 y = 5

and

3 x + 7 y = 17

, giving

P (1, 2)

. Among lines through

P

, the one farthest from the origin is perpendicular to

O P

P

. Since

Q (3, 6) = 3 (1, 2)

lies on the line

O P

, its distance to this perpendicular line equals

P Q = (3 - 1)^{2} + (6 - 2)^{2} = 20

. Hence

d^{2} = 20

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Single correct option

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