Straight Line Question 237

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:

Options:

A) (a, b) (b)

B) (b, a)

C) (a, -b) (d)

D) (-a, b)

Show Answer

Answer:

Correct Answer: A

Solution:

  • [a] Given equation of stating lines are $ x+2y-9=0,3x+5y-5=0 $ and $ ax+by-1=0 $ They are concurrent, if $ -5+5b-2(-3+5a)-9(3b-5a)=0 $

$ \Rightarrow 35a-22b+1=0 $ Thus, given straight lines are concurrent if the straight line $ 35x-22y+1=0 $ passes through (a, b).