Solveeit Logo
Login

Question

Mathematics Question on Straight lines

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

(a,-b)

C

(-a,b)

D

(a,b)

Answer

(a,b)

Explanation

Solution

The correct answer is option (D) : (a,b)
The three lines are concurrent if
∣12−9 35−5 ab−1∣=0\begin{vmatrix} 1 &2 &-9 \\\ 3&5 &-5 \\\ a&b &-1 \end{vmatrix}=0
⇒35a−22b+1⇒35x−22y+1=0\Rightarrow 35a-22b+1\Rightarrow 35x-22y+1=0 passes through (a,b)