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

A
$(a, b)$
B
$(b, a)$
C
$(- a, - b)$
D
none of these

Solution:

The three lines are concurrent if
$|\begin{array}{rrr} 1 2 - 9 \\ 3 5 - 5 \\ a b - 1 \end{array}| = 0$
$\Rightarrow$ $35 a - 22 b + 1 = 0$
which is true if the line $35 x - 22 y + 1 = 0$ passes through (a, b).

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