The value of - for which the lines 2x-5y-3-0- 5x-9y-0 and x-2y-1-0 are concurrent is -

If the given lines are concurrent, then determinant of coefficient matrix will be zero. ⇒2 535 9λ1 21=0⇒2 9+2λ+55 λ+3 10+9=0⇒ 18+4λ+25 5λ 3=0⇒4 λ=0⇒λ=4 ...

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Standard XII

Mathematics

Slope Intercept Form of a Line

The value of ...

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 .

-1

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-4

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Solution

The correct option is D 4
If the given lines are concurrent, then determinant of coefficient matrix will be zero.
$\Rightarrow ⎛ ⎜ ⎝ \begin{matrix} 2 & - 5 & 3 5 & - 9 & λ 1 & - 2 & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow 2 (- 9 + 2 λ) + 5 (5 - λ) + 3 (- 10 + 9) = 0 \Rightarrow - 18 + 4 λ + 25 - 5 λ - 3 = 0 \Rightarrow 4 - λ = 0 \Rightarrow λ = 4$

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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 correct option is D 4If 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