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JEE Main20258 Apr 2025Evening ShiftMathematicsStraight LinesActual

Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle with the positive x -axis and the equations of its diagonals are ( 3 +1) x+( 3 -1) y=0 and ( 3 -1) x-( 3 +1) y+8 3 =0 . Then a ^2 is equal to

Options

  1. A48
  2. B32
  3. C16
  4. D24

Correct answer

A. 48

Step-by-step solution

aligned & Slope of diagonal OB = 3 +1 1- 3 & = 105^ & =60^ & A ( acos 60^ , asin 60^ ) & A ( a 2 , 3 a 2 ) aligned A Lies on other diagonal aligned & ( 3 -1 2 ) a- ( 3 +1 2 ) 3 a+8 3 =0 & a [ 3 -1-3- 3 2 ]=-8 3 & a=4 3 & a^2=48 aligned

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