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

Question

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

Smart Achievers · Accepted Answer

(1)

For $x + 2 y - 9 = 0$ , $3 x + 5 y - 5 = 0$ , $a x + b y - 1 = 0$

to be concurrent $| \begin{matrix} 1 & 2 & - 9 \\ 3 & 5 & - 5 \\ a & b & - 1 \end{matrix} |$ $= 0$

$\Rightarrow$ $35 a - 22 b + 1 = 0$ ...(i)

Comparing (i) with equation $35 x - 22 y + 1 = 0 .$

Hence line $35 x - 22 y + 1 = 0$ should pass through $(a, b)$ .

Solution

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

1 $(a, b)$

2 $(b, a)$

3 $(a, - b)$

4 $(- a, b)$

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Solution

Q. 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

1 (a,b)

2 (b,a)

3 (a,-b)

4 (-a,b)