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A family of lines is given by (1 + 2λ)x + (1 - λ)y + λ = 0, λ being the parameter. The line belonging to this family at the maximum

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A  family of lines is given by (1 + 2λ)x + (1 - λ)y + λ = 0, λ being the parameter. The line belonging to this family at the maximum distance from the pt (1,4) is

(a)  4x - y + 1= 0

(b)  33x + 12y + 7 = 0

(c) 12x + 33y = 7

(d)  None of these. 

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Best answer

Correct option  (c) 12x + 33y = 7.

Explanation:

x + y + λ(2x - y + 1) = 0

The required line is y

12x + 33y = 7.

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