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MHT CET202616 April 2026Evening ShiftMathematicsStraight LinesActual

The line (2 + k)x + (1 + k)y = 5 + 7k passes through the fixed point for different values of k. If 'd' is the distance of a fixed point from the origin, then d^2 =

Options

  1. A29
  2. B37
  3. C65
  4. D85

Correct answer

D. 85

Step-by-step solution

The given equation of the line is (2 + k)x + (1 + k)y = 5 + 7k . Rearranging the terms to express it in the form L₁ + kL₂ = 0 : 2x + kx + y + ky - 5 - 7k = 0 (2x + y - 5) + k(x + y - 7) = 0 This represents a family of lines passing through the point of intersection of the lines: 2x + y - 5 = 0 x + y - 7 = 0 Solving these two equations simultaneously, we subtract the second equation from the first: (2x + y - 5) - (x + y - 7) = 0 x + 2 = 0 x = -2 Substituting x = -2 into the second equation: -2 + y - 7 = 0 y = 9 The

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