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MHT CET202525 Apr 2025Morning ShiftMathematicsStraight LinesActual

A line passes through P (-4,1) and meets the co-ordinate axes at points A and B . If P divides the segment A B internally in the ratio 1: 2 , then the equation of the line is

Options

  1. Ax-2 y+6=0
  2. Bx+10 y-6=0
  3. C2 x+y+4=0
  4. Dx-y+5=0

Correct answer

A. x-2 y+6=0

Step-by-step solution

The line with intercept form x a + y b = 1 intersects the axes at A(a, 0) and B(0, b) . Given that P(-4, 1) divides AB internally in the ratio 1:2 , the section formula yields 2a 3 = -4 for the x-coordinate and b 3 = 1 for the y-coordinate. Solving gives a = -6 and b = 3 . Substituting into the intercept form provides x -6 + y 3 = 1 . Multiplying through by 6 and rearranging yields x - 2y + 6 = 0 , which corresponds to option A. Answer: A

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