First slide

Equation of line in Straight lines

Question

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

Moderate

A

$(a, b)$
B

$(b, a)$
C

$(a, - b)$
D

$(- a, b)$

Solution

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

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