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The sum of the intercepts on the coordinate axes made by a line passing through the point a , b and the common point of x a + y b = 1 and x b + y a = 1 is

Options

  1. Aa - b 2 a + b a b
  2. Bb - a a 2 - b 2 a b
  3. Ca + b a 2 - b 2 a b
  4. Da - b a 2 + b 2 a b

Correct answer

B. b - a a 2 - b 2 a b

Step-by-step solution

Point of intersection of x a + y b = 1 and x b + y a = 1 is a b a + b , a b a + b Now, line joining a , b and a b a + b , a b a + b is y - b x - a = a b a + b - b a b a + b - a ⇒ y - b a 2 = b 2 x - a ⇒ x a b - a b + y b a - b a = 1 ⇒ sum of the x intercept and the y intercept is equal to a b - a b + b a - b a = b - a a 2 - b 2 a b

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