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MHT CET202620 April 2026Morning ShiftMathematicsPair of LinesActual

If the equation 16x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0 represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........

Options

  1. A4x - 3y - 1 = 0
  2. B4x - 3y + 1 = 0
  3. C8x - 6y - 1 = 0
  4. D8x - 6y + 1 = 0

Correct answer

A. 4x - 3y - 1 = 0

Step-by-step solution

The given equation is 16x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0 . This can be rewritten by grouping the terms as: (4x - 3y)^2 - 2(4x - 3y) - 35 = 0 Let t = 4x - 3y . The equation becomes: t^2 - 2t - 35 = 0 (t - 7)(t + 5) = 0 t = 7 or t = -5 Substituting back t = 4x - 3y , the equation represents two parallel straight lines: 4x - 3y - 7 = 0 and 4x - 3y + 5 = 0 The locus of points equidistant from these two parallel lines is a line parallel to them and lying exactly midway between them. Its equation is given by the arit

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