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AP EAMCET202120 Aug 2021Evening ShiftMathematicsStraight LinesActual

The point to which the origin should be shifted in order to eliminate the x and y terms from the equation 9 x 2 + 4 y 2 + 10 x + 12 y + 1 = 0 is

Options

  1. A5 9 , 3 2
  2. B- 5 2 , - 3 9
  3. C- 5 9 , - 3 2
  4. D- 3 2 , - 5 9

Correct answer

C. - 5 9 , - 3 2

Step-by-step solution

Let the origin be shifted at h , k Let x ' , y '   be the new co-ordinate ∴   x = x ' + h     & y = y ' + k ∵   Given equation is 9 x 2 + 4 y 2 + 10 x + 12 y + 1 = 0 Put x = x ' + h   & y = y ' + k ⇒   9 x ' + h 2 + 4 y ' + k 2 + 10 x ' + h + 12 y ' + k + 1 = 0 ⇒ 9 x ' 2 + 9 h 2 + 18 x ' h + 4 y ' 2 + 4 k 2 + 8 y ' k + 10 x ' + 10 h + 12 y ' + 12 k + 1 = 0 ⇒   9 x ' 2 + 4 y '

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