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AP EAMCET20224 Jul 2022Morning ShiftMathematicsStraight LinesActual

Starting from the point A - 3 , 4 , a moving object touches 2 x + y - 7 = 0 at B and reaches the point C 0 , 1 . If the object travels along the shortest path, the distance between A and B is

Options

  1. A9 170 25
  2. B9 5
  3. C3 2
  4. D6 5

Correct answer

A. 9 170 25

Step-by-step solution

Given, Point A - 3 , 4 and C 0 , 1 and let moving point be B x , y Now given equation of line 2 x + y = 7 ⇒ y = - 2 x + 7               . . . 1 Now finding distance we get, A B + B C = x + 3 2 + y - 4 2 + x - 0 2 + y - 1 2               . . . 2 Now substituting the value of y in (2) we get, = x + 3 2 + - 2 x + 7 - 4 2 + x - 0 2 + - 2 x + 7 - 1 2 = x 2 + 9 + 6 x + 4 x 2 + 9 - 12 x + x 2 + 4 x 3 + 36 - 24 x = 5 x 2 - 6 x + 18 + 5 x 2 - 24 x +

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