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

(a,b)

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(b,a)

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(−a, b)

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(−a, −b)

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Solution

The correct option is B
(b,a)

Given lines are concurrent
$\begin{matrix} 1 & 2 & - 9 | 3 & 5 & - 5 | & = 0 a & b & - 1 \end{matrix}$
$\Rightarrow$ 35a - 22b + 1 = 0
$\Rightarrow$ 22b - 35a - 1 = 0
Given equation is 22x - 35y - 1 = 0
By comparison (x,y) = (b,a)
$∴$ Given line must passes through (b,a)

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