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AP EAMCET202023 Sep 2020Morning ShiftMathematicsStraight LinesActual

The point to which the origin should be shifted so that the equation y 2 - 6 y - 4 x + 13 = 0 will not contain any term in y and the constant term, is

Options

  1. A1 ,   1
  2. B1 ,   2
  3. C2 ,   1
  4. D1 ,   3

Correct answer

D. 1 ,   3

Step-by-step solution

Given equation, y 2 - 6 y - 4 x + 13 = 0 Now origin is shifted to (h,k) y → y + k   2 x → x + h k ( y + k ) 2 - 6 ( y + k ) - 4 ( x + h ) + 13 = 0 y 2 + k 2 + 2 k y - 6 y - 6 k - 4 x - 4 h + 13 = 0 y 2 will not contain any term y 2 + 2 k - 6 y = 0   &   k 2 - 6 k - 4 h + 13 = 0 y ( y + 2 k - 6 ) = 0                         ( 3 ) 2 - 6 ( 3 ) - 4 h + 13 = 0 y = 0   / y + 2 k - 6 = 0           9 - 1

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