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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

A line passing through the point A 2,2 encloses an area of 4 sq. units with coordinate axes. The distance (in units) of the origin from the line is equal to

Options

  1. A1
  2. B2 2
  3. C2
  4. D2

Correct answer

C. 2

Step-by-step solution

Let, the equation of the line is x a + y b = 1 ⇒ 2 a + 2 b = 1 ⇒ 2 b + a = a b … . i Case I: 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 ⇒ No ‘ a ’ is possible (Discriminant is negative) Case II: If intercept are of opposite sign, then - 1 2 a b = 4 ⇒ a b = - 8 ⇒ b + a = - 8 2 = - 4 ⇒ a 2 + b 2 = 16 - 2 - 8 = 32 ⇒ the distance of origin from the line is a b a 2 + b 2 = 8 32

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