Straight Line Question 142

Question: The condition on a and b, such that the portion of the line $ ax+by-1=0 $ intercepted between the lines $ ax+y=0 $ and $ x+by=0 $ subtends a right angle at the origin, is

Options:

A) $ a=b $

B) $ a+b=0 $

C) $ a=2b $

D) $ 2a=b $

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Answer:

Correct Answer: B

Solution:

  • [b] Lines $ ax+y=0 $ and $ x+by=0 $ intersect at O(0,0). Hence, if AB subtends right angle at O(0,0), then $ ax+y=0 $ and $ x+by=0 $ are perpendicular to each other so, $ (-a)( -\frac{1}{b} )=-1 $ Or $ a+b=0 $