Straight Line Question 337

Question: The equation to the straight line passing through the point of intersection of the lines $ 5x-6y-1=0 $ and $ 3x+2y+5=0 $ and perpendicular to the line $ 3x-5y+11=0 $ is [MP PET 1994]

Options:

A) $ 5x+3y+8=0 $

B) $ 3x-5y+8=0 $

C) $ 5x+3y+11=0 $

D) $ 3x-5y+11=0 $

Show Answer

Answer:

Correct Answer: A

Solution:

  • The point of intersection of $ 5x-6y-1=0 $ and $ 3x+2y+5=0 $ is $ (-1,-1) $ . Now the line perpendicular to $ 3x-5y+11=0 $ is $ 5x+3y+k=0 $ , but it passes through $ (-1,-1) $
    Þ $ -5-3+k=0\Rightarrow k=8 $ Hence required line is $ 5x+3y+8=0 $ .