1
Question
The value of λ for which the lines 2x-5y+3=0, 5x-9y+λ=0 and x-2y+1=0 are concurrent is
The value of λ for which the lines 2x-5y+3=0, 5x-9y+λ=0 and x-2y+1=0 are concurrent is
Open in App
Solution
The correct option is D 4
If the given lines are concurrent, then determinant of coefficient matrix will be zero.
⇒⎛⎜⎝2−535−9λ1−21∣∣
∣∣=0⇒2(−9+2λ)+5(5−λ)+3(−10+9)=0⇒−18+4λ+25−5λ−3=0⇒4−λ=0⇒λ=4
If the given lines are concurrent, then determinant of coefficient matrix will be zero.
⇒⎛⎜⎝2−535−9λ1−21∣∣ ∣∣=0⇒2(−9+2λ)+5(5−λ)+3(−10+9)=0⇒−18+4λ+25−5λ−3=0⇒4−λ=0⇒λ=4