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MHT CET202618 April 2026Evening ShiftMathematicsPair of LinesActual

The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by x^2 - 6xy + 5y^2 + 10x - 14y + 9 = 0 is

Options

  1. Axy + 2x + y + 2 = 0
  2. Bxy + 2x - y - 2 = 0
  3. Cxy - 2x + y - 2 = 0
  4. Dxy - 2x - y + 2 = 0

Correct answer

D. xy - 2x - y + 2 = 0

Step-by-step solution

Let the given equation be S = x^2 - 6xy + 5y^2 + 10x - 14y + 9 = 0 . The point of intersection of the pair of straight lines represented by S = 0 can be found by solving the partial derivatives S x = 0 and S y = 0 . S x = 2x - 6y + 10 = 0 x - 3y + 5 = 0 S y = -6x + 10y - 14 = 0 3x - 5y + 7 = 0 Solving the two linear equations: From the first equation, x = 3y - 5 . Substituting into the second equation: 3(3y - 5) - 5y + 7 = 0 9y - 15 - 5y + 7 = 0 4y - 8 = 0 y = 2 Substituting y = 2 back into x = 3y - 5 , we get x =

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