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Question

The equation x2+(λ+μ)xy+λμy2+x+μy=0 represents two parallel straight lines if

A
λ+μ=0
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B
λ=4μ
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C
λ=μ
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D
none of these
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Solution

The correct option is C λ=μ
Let take two parrallel lines are ax+by+c1=0 and ax+by+c2=0
So, the combined equation is
a2x2+2abxy+b2y2+ax(c1+c2)+by(c1+c2)+c1c2=0 and compare with given equation
By comparison
λ+μ=2ab,λμ=b2
By solving, get (λμ)2=0
Hence,λ=μ

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