The members of the family of lines - - x-2- - y- -2- where - 0- 1- pass through the point

The correct option is A (3, 1) (λ +μ )x+(2λ +μ )y=λ +2μ ⇒( x+2y 1 ) λ +( x+y 2 ) μ =0 Solving x+2y 1=0 and x+y 2=0 we get intersecti ...

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Standard XII

Mathematics

Condition for Concurrency of Three Lines

The members o...

Question

The members of the family of lines $(λ + μ) x + (2 λ + μ) y = λ + 2 μ$ , where $λ \neq 0, μ \neq 1,$ pass through the point

(3, - 1)

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(- 3, 1)

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(1, 1)

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none of these

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Solution

The correct option is A $(3, - 1)$
$(λ + μ) x + (2 λ + μ) y = λ + 2 μ \Rightarrow (x + 2 y - 1) λ + (x + y - 2) μ = 0$
Solving $x + 2 y - 1 = 0$ and $x + y - 2 = 0$ we get intersection point as $(3, - 1) .$

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The members of the family of lines (λ+μ)x+(2λ+μ)y=λ+2μ, where λ≠0,μ≠1, pass through the point

The correct option is A (3,−1)(λ+μ)x+(2λ+μ)y=λ+2μ⇒(x+2y−1)λ+(x+y−2)μ=0Solving x+2y−1=0 and x+y−2=0 we get intersection point as (3,−1).

The members of the family of lines $(λ + μ) x + (2 λ + μ) y = λ + 2 μ$ , where $λ \neq 0, μ \neq 1,$ pass through the point

The correct option is A $(3, - 1)$
$(λ + μ) x + (2 λ + μ) y = λ + 2 μ \Rightarrow (x + 2 y - 1) λ + (x + y - 2) μ = 0$
Solving $x + 2 y - 1 = 0$ and $x + y - 2 = 0$ we get intersection point as $(3, - 1) .$