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BITSAT2014MathematicsStraight LinesActual

If P₁ and P₂ be the length of perpendiculars from the origin upon the straight lines x +y cosec =a and x -y =a 2 respectively, then the value of 4 P ₁²+ P ₂²

Options

  1. Aa²
  2. B2 a²
  3. Ca² / 2
  4. D3 a²

Correct answer

A. a²

Step-by-step solution

We have P₁= length of perpendicular from (0,0) on x +y cosec =a aligned i.e. P₁ &= | a ² + e c² |=|a | &= | a 2 2 | or 2 P₁=|a 2 | aligned P ₂= Length of the perpendicular from (0,0) on x -y =a 2 ₂= | a 2 ² + ² |=|a 2 | Now, 4 P₁²+P₂²=a² ² 2 +a² ² 2 =a²

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