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JEE Main2014MathematicsStraight LinesActual

If a line L is perpendicular to the line 5 x - y = 1 , and the area of the triangle formed by the line L and the coordinate axes is 5 sq units, then the distance of the line L from the line x + 5 y = 0 is

Options

  1. A7 1 3 units
  2. B7 5 units
  3. C5 1 3 units
  4. D5 7 units

Correct answer

C. 5 1 3 units

Step-by-step solution

The equation of a line perpendicular to the line a x + b y + c = 0 is b x - a y + k = 0 ,   k ∈ R . Given, line L is perpendicular to 5 x - y = 1 , hence the equation of L is x +5 y + k =0 For finding x -Intercept, put y = 0 ⇒ x + k = 0 ,       ⇒ x = - k ∴ x -intercept = - k Similarly, for finding y - Intercept, put x = 0 ⇒ 5 y + k = 0 ,     ⇒ y = - k 5 ∴ y -intercept = - k 5 Given, the area formed by the line L with the coordinate axes is 5 sq

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