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MHT CET202618 April 2026Morning ShiftMathematicsStraight LinesActual

The line L₁ given by x p + y 2 = 1 passes through the point (5,0) . The line L₂ given by x 10 + y q = 1 is parallel to L₁ . Then the distance between the lines L₁ and L₂ is...

Options

  1. A10 29
  2. B19 2 29
  3. C5 41
  4. D10 41

Correct answer

A. 10 29

Step-by-step solution

Since the line L₁ given by x p + y 2 = 1 passes through (5,0) , substituting these coordinates gives: 5 p + 0 = 1 p = 5 The equation of L₁ becomes x 5 + y 2 = 1 , which simplifies to 2x + 5y - 10 = 0 . The line L₂ given by x 10 + y q = 1 is parallel to L₁ . Equating their slopes: - q 10 = - 2 5 q = 4 The equation of L₂ becomes x 10 + y 4 = 1 , which simplifies to 4x + 10y - 40 = 0 or 2x + 5y - 20 = 0 . The perpendicular distance between the parallel lines 2x + 5y - 10 = 0 and 2x + 5y - 20 = 0 is: d = |-10 - (-20)|

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