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Question

The equation of one of the lines represented by the pair of lines 12x210xy+2y2+11x5y+2=0 is/are

A
6x2y+1=0
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B
3xy+2=0
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C
2xy+2=0
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D
4x2y+1=0
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Solution

The correct option is D 4x2y+1=0
12x210xy+2y2=0
(6x2y)(2xy)=0

So, required equations will be of the form
6x2y+λ1=0 & 2xy+λ2=0
Now,
(6x2y+λ1)(2xy+λ2)=12x210xy+2y2+11x5y+2

By comparing coefficients,
6λ2+2λ1=112λ2+λ1=5λ1=4 and λ2=12line equations are3xy+2=0 and 4x2y+1=0

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