Question

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

• A. (a, b)
• B. (b, a)
• C. (a, - b)
• D. (- a, b)

Answer 1

Answer: (A)

Given equation of straingh lines are x + 2y - 9 = 0, 3x + 5y - 5 = 0 and ax + by - 1 = 0
They are concurrent if $\left|\begin{array}{ccc}1& 2& -9\\ 3& 5& -5\\ a& b& -1\end{array}\right|=0$
$\Rightarrow -5+5b-2(-3+5a)-9(3b-5a)=0$
$\Rightarrow -5+5b+6-10a-27b+45a=0$
$\Rightarrow 35a-22b+1=0$
Thus, given straight lines are concurrent if the straight line 35x - 22y + 1 = 0 passes through (a, b).