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JEE Main20236 Apr 2023Morning ShiftMathematicsStraight LinesActual

The straight lines l 1 and l 2 pass through the origin and trisect the line segment of the line L : 9 x + 5 y = 45 between the axes. If m 1 and m 2 are the slopes of the lines l 1 and l 2 , then the point of intersection of the line y = ( m 1 + m 2 ) x with L lies on

Options

  1. Ay – 2 x = 5
  2. B6 x + y = 10
  3. Cy – x = 5
  4. D6 x – y = 15

Correct answer

C. y – x = 5

Step-by-step solution

Given, The straight lines l 1 and l 2 pass through the origin and trisect the line segment of the line L : 9 x + 5 y = 45 between the axes, And m 1 and m 2 are the slopes of the lines l 1 and l 2 , Now on plotting the diagram we get, Given equation of line, L : 9 x + 5 y = 45 ⇒ x 5 + y 9 = 1 Now using the section formula between point A 5 , 0   &   B 0 , 9 we get the value of point C   &   D ⇒ C ≡ 10 3 , 3 and D ≡ 5 3 , 6 Now finding the slope m 1   & &#1

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