The straight lines $x + 2 y - 9, 3 x + 5 y - 5 = 0$ and $a x + b y - 1 = 0$ are concurrent, if the straight line $35 x - 22 y + 1 = 0$ passes through the point

(a, b)

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(b, a)

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(- a, - b)

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None of these

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Solution

The correct option is A $(a, b)$
$x + 2 y - 9 = 0..... (i)$
$3 x + 5 y - 5 = 0.... (i i)$
$a x + b y - 1 = 0...... (i i i)$
Intersection of $(i)$ and $(i i)$ is $y = 22$ and $x = - 2 (22) + 9 = - 35$
Putting this point in $a x + b y - 1 = 0$ , we get $35 a - 22 b + 1 = 0$
For the three lines to be concurrent $35 x - 22 y + 1 = 0$ should pass through $(a, b)$

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