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AP EAMCET202318 May 2023Morning ShiftMathematicsHyperbolaActual

The equation of the pair of asymptotes of the hyperbola x^2-2 y^2-8 x+8 y+4=0 is

Options

  1. Ax^2-2 y^2-8 x+8 y-8=0
  2. B2 x^2-4 y^2-16 x+16 y-7=0
  3. Cx^2-2 y^2-8 x+8 y+8=0
  4. D2 x^2-4 y^2-16 x+16 y+9=0

Correct answer

C. x^2-2 y^2-8 x+8 y+8=0

Step-by-step solution

x^2-2 y^2-8 x+8 y+4=0 aligned & (x-4)^2-2(y-2)^2-16 & (x-4)^2-2(y-2)^2=4 aligned Then, the equation of asymptote is aligned & (x^2-4 )^2-2(y-2)^2=0 & x^2+16-8 x-2 y^2+8 y-8=0 & x^2-2 y^2-8 x+8 y+8=0 aligned

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