If the straight line $x + 2 y = 9, 3 x - 5 y = 5 & a x + b y = 1$ are concurrent, then the straight line $5 x + 2 y = 1$ passes through the point

(a, - b)

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(- a, b)

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(a, b)

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(- a, - b)

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Solution

The correct option is C $(a, b)$
Given lines
$x + 2 y = 9$
On comparing above eq with $a x + b y + c = 0$
$a_{1} = 1, b_{1} = 2, c_{1} = - 9$

$3 x - 5 y - 5 = 0$
On comparing above eq with $a x + b y + c = 0$
$a_{2} = 3, b_{2} = - 5, c_{2} = - 5$

$a x + b y - 1 = 0$
On comparing above eq with $a x + b y + c = 0$
$a_{3} = a, b_{3} = b, c_{3} = - 1$
Given lines are concurrent SO by formula
$∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ = 0$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & - 9 3 & - 5 & - 5 a & b & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$5 + 5 b - 10 a + 6 - 27 b - 45 a = 0$
$- 55 a - 22 b + 11 = 0$
$5 a + 2 b = 1$
On comapring above eq with $5 x + 2 y = 1$ we get
$x = a, y = b$
Hence line passes through $(a, b)$

Suggest Corrections

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