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Manipal MET2015MathematicsStraight Lines

One possible condition for the three points (a, b),(b, a) and (a^2,-b^2 ) to be collinear, is

Options

  1. Aa-b=2
  2. Ba+b=2
  3. Ca=1+b
  4. Da=1-b

Correct answer

C. a=1+b

Step-by-step solution

Given points will be collinear, if | array ccc a & b & 1 b & a & 1 a^2 & -b^2 & 1 array |=0 | array ccc a & b & 1 b-a & a-b & 0 a^2-a & -b^2-b & 0 array |=0 [applying R₂ R₂-R₁, R₃ R₃-R₁ ] array lr & (a-b) | array ccc a & b & 1 -1 & 1 & 0 a^2-a & -b^2-b & 0 array |=0 & (a-b) (b^2+b-a^2+a )=0 array array rr & (a-b) (a+b)- (a^2-b^2 ) =0 & (a-b)(a+b)(1-a+b)=0 & a=b or a+b=0 or a=1+b array

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