Q. 85.0( 2 Votes )

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

A. 0

B. 1

C. 2

D. infinite

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(-λ^{2} – 12) = 0

⇒ 6 + λ + 4λ – 8 – 3λ^{2} – 36 = 0

⇒ 5λ – 3λ^{2} – 38 = 0

⇒ 3λ^{2} – 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.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Various Forms of Equations of line45 mins

Slope, inclination and angle between two lines48 mins

Interactive Quiz on Equations of line23 mins

Parametric Equations of Straight line48 mins

Straight line | Analyse your learning through quiz56 mins

General Equation of a line43 mins

Motion in a Straight Line - 0665 mins

Motion in a Straight Line - 0556 mins

Motion in a Straight Line - 0372 mins

Motion in a Straight Line - 1169 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation