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Question

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

A
33x+12y7=0
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B
33x+12y+7=0
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C
12x+33y7=0
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D
12x+33y+7=0
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Solution

The correct option is C 12x+33y7=0
Given : (1+2λ)x+(1λ)y+λ=0
x+y+λ(2xy+1)=0
Clearly, it represents a family of lines passing through the intersection of the lines x+y=0 and 2xy+1=0 i.e., the point (13,13)


The required line passes through (13,13) and is perpendicular to the line joining (1,4) and (13,13)
So, its equation is
y13=1+13413(x+13)3y13=411(x+13)12x+33y7=0

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