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COMEDK2021MathematicsStraight Lines

The slopes of the lines, which make an angle 45^ with the line 3 x-y=-5 , are

Options

  1. A1,-1
  2. B1 2 ,-1
  3. C1, 1 2
  4. D-2, 1 2

Correct answer

D. -2, 1 2

Step-by-step solution

The given line is 3x - y = -5 , which can be written in the slope-intercept form y = 3x + 5 . The slope of this line is m₁ = 3 . Let the slope of the required lines be m . The angle between the lines is given as 45^ . Using the formula for the angle between two lines, = | m - m₁ 1 + m m₁ | , we have: 45^ = | m - 3 1 + 3m | 1 = | m - 3 1 + 3m | This leads to two cases: Case 1: m - 3 1 + 3m = 1 m - 3 = 1 + 3m -2m = 4 m = -2 Case 2: m - 3 1 + 3m = -1 m - 3 = -1 - 3m 4m = 2 m = 1 2 The slopes of the lines are -2 and 1

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