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AP EAMCET202018 Sep 2020Morning ShiftMathematicsStraight LinesActual

To which point the origin is to be shifted in order to eliminate first powers of (x ) and (y ) ( (x^1 ) and (y^1 ) terms) from the equation (4 x^2+9 y^2-8 x+36 y+4=0 ) ?

Options

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

Correct answer

C. ((1,-2) )

Step-by-step solution

Given equation is ( aligned & & 4 x^2+9 y^2-8 x+36 y+4 & =0 & & 4(x-1)^2+9(y+2)^2 & =36 & & (x-1)^2 9 + (y+2)^2 4 & =1 aligned ) If we shift the origin to ((l,-2) ), the equation reduce to ( x^2 9 + y^2 4 =1 ) and it is free from (x ) and (y ) terms.

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