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COMEDK2025MathematicsStraight LinesActual

If the line (3 x+14 y+7)+k(5 x+7 y+6)=0 is perpendicular to x -axis then the value of ' k ' is

Options

  1. A-2
  2. B- 3 5
  3. C1 3
  4. D2

Correct answer

A. -2

Step-by-step solution

The given equation of the line is (3x + 14y + 7) + k(5x + 7y + 6) = 0 . Rearranging the terms to group x and y coefficients: (3 + 5k)x + (14 + 7k)y + (7 + 6k) = 0 . A line is perpendicular to the x -axis if it is a vertical line, which means the coefficient of y must be zero and the coefficient of x must be non-zero. Setting the coefficient of y to zero: 14 + 7k = 0 . 7k = -14 . k = -2 . Checking the coefficient of x for k = -2 : 3 + 5(-2) = 3 - 10 = -7 , which is not zero. Thus, the line is indeed vertical. Answer

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