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COMEDK2025MathematicsStraight LinesActual

The intercept cut off by a line from y -axis is twice that from x -axis and the line passes through the point (1,2) , then the equation of a line is

Options

  1. A2 x-y=4
  2. B2 x+y-4=0
  3. C2 x-y+4=0
  4. D2 x+y+4=0

Correct answer

B. 2 x+y-4=0

Step-by-step solution

Let the intercept on the x -axis be a . According to the problem, the intercept on the y -axis is 2a . The intercept form of the line is x a + y 2a = 1 . Multiplying by 2a , we get 2x + y = 2a . Since the line passes through the point (1, 2) , we substitute x = 1 and y = 2 into the equation: 2(1) + 2 = 2a 4 = 2a a = 2 . Substituting a = 2 back into the equation 2x + y = 2a , we get 2x + y = 2(2) , which simplifies to 2x + y = 4 or 2x + y - 4 = 0 . Answer: 2 x+y-4=0

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