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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



Correct Answer
A

0

Your Answer
B

1

Your Answer
C

2

Your Answer
D

Infinite


Solution

The correct option is C

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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