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COMEDK2024Morning ShiftMathematicsStraight LinesActual

The perpendicular distance of a line from the origin is 5 units and its slope is -1 . The equation of the line is

Options

  1. Ax+y 2 5 =0
  2. Bx-y 5 2 =0
  3. Cx+y 5 2 =0
  4. Dx-y 2 5 =0

Correct answer

C. x+y 5 2 =0

Step-by-step solution

The equation of a line with slope m = -1 can be written in the form y = mx + c , which is y = -x + c or x + y - c = 0 . The perpendicular distance d of the line Ax + By + C = 0 from the origin (0, 0) is given by d = |C| A^2 + B^2 . Here, A = 1 , B = 1 , and C = -c . The distance d = 5 . Substituting the values into the formula: 5 = |-c| 1^2 + 1^2 = |c| 2 . This gives |c| = 5 2 , so c = 5 2 . Substituting c back into the equation x + y - c = 0 , we get x + y - ( 5 2 ) = 0 , which simplifies to x + y 5 2 = 0 . Answer

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