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
- A7 1 3 units
- B7 5 units
- C5 1 3 units
- 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