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Question

The number of real values of λ for which the lines x2y+3=0, λ x+3y+1=0 and 4xλy+2=0 are concurrent is


A

0

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B

1

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C

2

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D

Infinite

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Solution

The correct option is A

0


The given lines are

x2y+3=0 ...(1)

λx+3y+1=0 ...(2)

4xλy+2=0 ...(3)

It is given that (1), (2) and (3) are concurrent.

∣ ∣123λ314λ2∣ ∣=0

(6+λ)+2(2λ4)+3(λ212)=0

6+λ+4λ83λ236=0

5λ3λ238=0

3λ25λ+38=0

The discriminant of this equation is

254×3×38=431

Hence, there is no real value of 1 for which the lines x2y+3=0, λx+3y+1=0 and 4xλy+2=0 are concurrent.


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