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MHT CET20228 Aug 2022Evening ShiftMathematicsStraight LinesActual

The Centroid of the triangle formed by the lines 6 x^2+x y-y^2=0 and x+3 y-10=0 is

Options

  1. A( 1 3 , 7 3 )
  2. B(- 1 3 , -7 3 )
  3. C(- 1 3 , 7 3 )
  4. D( 1 3 , -7 3 )

Correct answer

C. (- 1 3 , 7 3 )

Step-by-step solution

aligned & 6 x^2+x y-y^2=0 & (3 x-y)(2 x+y)=0 & 3 x-y=0,2 x+y=0 & L₁ 3 x-y=0, L₂ 2 x+y=0 and L₃ x+3 y=10 & point of intersection of & L₁ and L₂ is (0,0), L₂ and L₃ is (-2,4), L₃ and L₁ is (1,3) & centroid of triangle ( 0-2+1 3 , 0+4+3 3 ) ( -1 3 , 7 3 ) aligned

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