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The portion of the line ax + by - 1 =0 , intercepted between the lines ax + by + 1 =0 and x+ by = 0 subtends a right angle at the origin and the condition in a and b is pa + b + b^2 =0 then find the value of p.
one year ago

Dear Abhinav

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

hence
p = 2

Regards
Arun (askIITians forum expert)
one year ago
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