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 point (1,4) is
A
4x−y+1=0
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B
33x+12y+7=0
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C
12x+33y=7
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D
None of these
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Solution
The correct option is B12x+33y=7 Here, x+y+λ(2x−y+1)=0 Since, each line passes through the point of intersection of the lines x+y=0 and 2x−y+1=0, which is (−13,13). Thus slope of the required line, m=−14−131+13=−411 Hence, the required line is y−13=−411(x+13)