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MHT CET202617 April 2026Evening ShiftMathematicsPair of LinesActual

If the equation ax^2 + 4xy - 2y^2 + 4x + 8y + 1 = 0 represents a pair of straight lines, then the coordinates of their point of intersection are.........

Options

  1. A( 1 2 , - 3 2 )
  2. B(- 3 2 , 1 2 )
  3. C( 1 2 , 3 2 )
  4. D(- 1 2 , 3 2 )

Correct answer

B. (- 3 2 , 1 2 )

Step-by-step solution

The given equation is S = ax^2 + 4xy - 2y^2 + 4x + 8y + 1 = 0 . Comparing with the general equation of second degree ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 , we get: a = a , h = 2 , b = -2 , g = 2 , f = 4 , c = 1 . For the equation to represent a pair of straight lines, the condition is = abc + 2fgh - af^2 - bg^2 - ch^2 = 0 . Substituting the values: a(-2)(1) + 2(4)(2)(2) - a(4)^2 - (-2)(2)^2 - 1(2)^2 = 0 -2a + 32 - 16a + 8 - 4 = 0 -18a + 36 = 0 a = 2 The point of intersection of the pair of straight lines is obtai

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