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AP EAMCET202316 May 2023Evening ShiftMathematicsHyperbolaActual

Let the transverse axis of a hyperbola H be parallel to the X- axis and x^2+y^2-2 x-4 y+3=0 be the equation of the auxiliary circle of H . If the asymptotes of H are at right angles, then the equation of the hyperbola is

Options

  1. A3 x^2-2 y^2-6 x+8 y-11=0
  2. Bx^2-y^2+2 x+4 y-5=0
  3. C3 x^2-2 y^2+6 x+8 y-11=0
  4. Dx^2-y^2-2 x+4 y-5=0

Correct answer

D. x^2-y^2-2 x+4 y-5=0

Step-by-step solution

Centre of auxiliary circle = centre of hyperbola =(1,2) length of transverse axis = Diameter of auxiliary circle =2 a =2 1+4-3 a = 2 A hyperbola whose asymptotes are at right angles to each other is rectangular hyperbola i.e. e = 2 Since, b^2=a^2 (e^2-1 )=2(2-1)=2 b= 2 Now, equation of hyperbola is (x-1)^2 2 - (y-1)^2 2 =1 x^2-y^2-2 x+4 y-5=0

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