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A line passing through the point 2 , 2 encloses an area of 4   s q .   u n i t s with coordinate axes. The sum of intercepts made by the line on the x and y axis is equal to

Options

  1. A– 2
  2. B4
  3. C– 4
  4. D2

Correct answer

C. – 4

Step-by-step solution

Let equation of line is x a + y b = 1 ⇒ 2 a + 2 b = 1 ⇒   2 b + a = a b ... 1 Case-1: If both intercepts are positive Then, 1 2 a b = 4 ⇒ a b = 8 ⇒ b + a = 4 ⇒   a 4 - a 8 ⇒ a 2 - 4 a + 8 = 0 ⇒ a 4 - a = 8 ⇒ No value of a is possible (Discriminant is negative) Case-2: If intercepts are of opposite sign, then - 1 2 a b = 4 ⇒ a b = - 8 ⇒ b + a = - 8 2 = - 4 ⇒ a - 4 - a = - 8 ⇒ a 2 + 4 a - 8 = 0 ⇒ a is possible hence b is possibl

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