The condition on `a` and `b` , such that the portion of the line `a x+b y-1=0` intercepted between the lines `a x+y=0` and `x+b y=0` subtends a right angle at the origin, is (a)`a=b` (b) `a+b=0` (c)`a=2b` (d) `2a=b`

Options

A. a =b
B. a+b=0
C. a=2b
D. 2a=b

Answer

B

Explanation

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)(-(1)/(b))=-1`
or a+b=0