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AP EAMCET2007MathematicsPair of Lines

In order to eliminate the first degree terms from the equation 2 x^2+4 x y+5 y^2-4 x-22 y+7=0 , the point to which origin is to be shifted, is

Options

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

Correct answer

C. (-2,3)

Step-by-step solution

Given equation is 2 x^2+4 x y+5 y^2-4 x-22 y+7=0 Here, a=2, b=5, c=7, h=2, g=-2, f=-11 To eliminate 1st degree terms origin is to be shifted to the point ( h f-b g a b-h^2 , g h-a f a b-h^2 ) aligned & = ( -22+10 10-4 , -4+22 10-4 ) & = ( -12 6 , 18 6 )=(-2,3) aligned

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