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JEE Main202225 Jul 2022Morning ShiftMathematicsStraight LinesActual

A line, with the slope greater than one, passes through the point A 4 , 3 and intersects the line x - y - 2 = 0 at the point B . If the length of the line segment A B is 29 3 , then B also lies on the line

Options

  1. A2 x + y = 9
  2. B3 x - 2 y = 7
  3. Cx + 2 y = 6
  4. D2 x - 3 y = 3

Correct answer

C. x + 2 y = 6

Step-by-step solution

Given point B lie on the line x - y - 2 = 0 , so the point will be B x 1 , x 1 - 2 Now given distance between A B is 29 3 , so by distance formula, x 1 - 4 2 + x 1 - 2 - 3 2 = 29 3 Now on squaring on both side we get, 18 x 1 2 - 162 x 1 + 340 = 0 On solving we get, x 1 = 51 9 or x 1 = 10 3 So, y 1 = 33 9 or y 1 = 4 3 Now we can see only x + 2 y = 6 will satisfy the point 10 3 , 4 3

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