question_answer

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

A) \[a=b\]

B) \[a+b=0\]

C) \[a=2b\]          

D) \[2a=b\]

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, \[(-a)\left( -\frac{1}{b} \right)=-1\] Or \[a+b=0\]