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JEE Main2015MathematicsStraight LinesActual

Let L be the line passing through the point P 1 , 2 such that its intercepted segment between the co-ordinate axes is bisected at P . If L 1 is the line perpendicular to L and passing through the point - 2 , 1 , then the point of intersection of L and L 1 is

Options

  1. A3 5 , 23 10
  2. B4 5 , 12 5
  3. C11 20 , 29 10
  4. D3 10 , 17 5

Correct answer

B. 4 5 , 12 5

Step-by-step solution

If P is the midpoint of the segment between the axes, them point A 2 ,   0 and B 0 ,   4 . The equation of the line is, x 2 + y 4 = 1 or, 2 x + y = 4       … 1 The line perpendicular to it is of form, x - 2 y = k Since it passes through ( - 2 ,   1 ) , - 2 - 2 = k ⇒ k = - 4 ∴ Line is, x - 2 y = - 4             … 2 Solving 1 and 2 we get 4 5 , 12 5 .

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