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The line L 1 : x 5 + y b = 1 passes through the point 13 , 32 and is parallel to L 2 : x c + y 3 = 1 . Then, the distance between L 1 and L 2 is

Options

  1. A17 units
  2. B17 15 units
  3. C23 17 units
  4. D23 15 units

Correct answer

C. 23 17 units

Step-by-step solution

Slope of the line L 1 = - b 5 and slope of the line L 2 = - 3 c . The line L 1 is parallel to the line L 2 ⇒ b 5 = 3 c ⇒ b c = 15 As 13 , 32 lies on L 1 , so 13 5 + 32 b = 1 ⇒ 32 b = - 8 5 ⇒ b = - 20 So, c = - 3 4 ∴ Equation of L 2 : y - 4 x = 3 Hence, distance between L 1 and L 2 = 52 - 32 + 3 17 = 23 17 units

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