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MHT CET202613 April 2026Evening ShiftMathematicsStraight LinesActual

The equation of the straight line passing through the point (-5, 3) such that the portion of the line intercepted between the axes is divided by the point in the ratio 4:3 (from the X-axis to the Y-axis) is...

Options

  1. A9x + 20y + 105 = 0
  2. B9x - 20y - 105 = 0
  3. C9x - 20y + 105 = 0
  4. D9x + 20y - 105 = 0

Correct answer

C. 9x - 20y + 105 = 0

Step-by-step solution

Let the line intersect the X-axis at A(a, 0) and the Y-axis at B(0, b) . The point P(-5, 3) divides the line segment AB in the ratio 4:3 from the X-axis to the Y-axis. Using the section formula, the coordinates of P are given by: P(x, y) = ( 4(0) + 3(a) 4 + 3 , 4(b) + 3(0) 4 + 3 ) = ( 3a 7 , 4b 7 ) Equating this to the given coordinates of P(-5, 3) : 3a 7 = -5 a = - 35 3 4b 7 = 3 b = 21 4 The equation of the line in intercept form is x a + y b = 1 . Substituting the values of a and b : x - 35 3 + y 21 4 = 1 - 3x 35

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