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JEE Main202127 Aug 2021Evening ShiftMathematicsStraight LinesActual

Let A ( a , 0 ) , B ( b , 2 b + 1 ) and C ( 0 , b ) , b ≠ 0 , | b | ≠ 1 , be points such that the area of triangle A B C is 1 sq. unit, then the sum of all possible values of a is:

Options

  1. A- 2 b b + 1
  2. B2 b 2 b + 1
  3. C- 2 b 2 b + 1
  4. D2 b b + 1

Correct answer

C. - 2 b 2 b + 1

Step-by-step solution

Given coordinates of triangle A B C , A ( a , 0 ) , B ( b , 2 b + 1 ) , C ( 0 , b ) Area = 1 2 a 0 1 b 2 b + 1 1 0 b 1 1 2 a ( b + 1 ) + b 2 = ± 1 a b + a + b 2 = ± 2 If 2 is positive a = 2 − b 2 b + 1 If 2   is negative a = − 2 − b 2 b + 1 Sum of possible values of a = 2 - b 2 b + 1 + - 2 - b 2 b + 1 = - 2 b 2 b + 1

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