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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


  1. 2a = b

  2. a = b

  3. a + b = 0

  4. a = 2b


Solution

The correct option is C

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) (1b)=1,

a + b = 0

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