Answer :

The given lines are


x 2y + 3 = 0 … (1)


λx + 3y + 1 = 0 … (2)


4x λy + 2 = 0 … (3)


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



(6 + λ) + 2(2λ – 4) + 3(-λ2 – 12) = 0


6 + λ + 4λ – 8 – 3λ2 – 36 = 0


5λ – 3λ2 – 38 = 0


3λ2 – 5λ + 38 = 0


The discriminant of this equation is 25-4 × 3 × 38 = -431


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

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