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COMEDK2022MathematicsStraight Lines

If 2 and 3 are intercepts of a line L=0 , then the distance of L 0 from the origin is

Options

  1. A5 13
  2. B13 6
  3. C6 13
  4. D1

Correct answer

C. 6 13

Step-by-step solution

The intercept form of a line with x-intercept a and y-intercept b is given by x a + y b = 1 . Given a = 2 and b = 3 , the equation of the line is x 2 + y 3 = 1 . Multiplying by 6, we get 3x + 2y = 6 , or 3x + 2y - 6 = 0 . The distance d of a line Ax + By + C = 0 from the origin (0,0) is given by d = |C| A^2 + B^2 . Substituting A = 3 , B = 2 , and C = -6 , we get d = |-6| 3^2 + 2^2 = 6 9 + 4 = 6 13 . Answer: 6 13

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