Question

Find the condition on a and b, such that the portion of the line ax+by-1=0, intercepted between the lines ax+y+1=0 and x+by=0 subtends a right angle at the origin.
(Please give a hint only) 

Answer 1

Let, ax+by-1=0 .........1. ax+y+1=0 …......2. x+by=0 .........3. Line passing through the common point of 1, 2 and through origin is 2ax+(1+b)y=0. Line passing through the common point of 1, 3 and through origin is x+by=0. The angle between these two lines is 90 degrees then (-2a/(1+b))(-1/b)=-1 You get it to be 2a+b+b²=0