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AP EAMCET202318 May 2023Evening ShiftMathematicsHyperbolaActual

The equation of the pair of asymptotes of the hyperbola (x-3)^2 3 - (y-2)^2 2 =1 is

Options

  1. A2 x^2-3 y^2-12 x+12 y-6=0
  2. B2 x^2-3 y^2-12 x+12 y+8=0
  3. C2 x^2-3 y^2-12 x+12 y-8=0
  4. D2 x^2-3 y^2-12 x+12 y+6=0

Correct answer

D. 2 x^2-3 y^2-12 x+12 y+6=0

Step-by-step solution

Equation of hyperbola is aligned & (x-3)^2 3 - (y-2)^2 2 =1 & 2 (x^2+9-6 x )-3 (y^2+4-4 y )=6 & 2 x^2-3 y^2-12 x+12 y+6=6 & 2 x^2-3 y^2-12 x+12 y=0 aligned Pair of asymptotes of the curve differs by the constant only. Equation of pair of asymptotes is : 2 x^2-3 y^2-12 x+12 y+ =0 which represents a pair of straight line if =a b c+2 f g h-a f^2-b g^2-c h^2=0 where a =2, ~b =-3, ~h =0, ~g =-6 f =6 c = Then, we have : aligned & 2 (-3) +2 6 (-6) 0-2(+6)^2-(-3)(-6)^2- & 0=0 =6 aligned Putting the value of in eq ^ n (i),

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