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MHT CET202522 Apr 2025Morning ShiftMathematicsStraight LinesActual

From the following options, the nearest line to the origin is ....

Options

  1. A3 x-4 y+4=0
  2. B2 x-3 y=5
  3. C4 x-3 y+12=0
  4. D5 x-2 y=3

Correct answer

D. 5 x-2 y=3

Step-by-step solution

Nearest Line to the Origin A line is nearest to the origin if it has the smallest perpendicular distance from the origin, calculated by d = |C| / A^2 + B^2 for the standard form Ax + By + C = 0 . For 3x - 4y + 4 = 0 : d = |4| / 9 + 16 = 4/5 = 0.8 For 2x - 3y - 5 = 0 : d = | -5 | / 4 + 9 5 / 3.605 1.387 For 4x - 3y + 12 = 0 : d = |12| / 16 + 9 = 12/5 = 2.4 For 5x - 2y - 3 = 0 : d = | -3 | / 25 + 4 3 / 5.385 0.557 Distances: 0.8, 1.387, 2.4, 0.557. The least is approximately 0.557 . The line 5x - 2y = 3 is nearest to

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