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

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

Answer 1

The correct option is B

a + b = 0

ax + y = 0

by + x = 0

Intersect at (0, 0)

If AB subtends right angle at (0, 0), then ax + y = 0 and x + by = 0 are perpendicular to each other.

So, (-a) $\left(\frac{-1}{b}\right)=-1,$

a + b = 0