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Manipal MET2011MathematicsHyperbola

The diameter of 16 x^2-9 y^2=144 which is conjugate to x=2 y is

Options

  1. Ay= 32 x 9
  2. Bx= 16 9 y
  3. Cy= 16 9 x
  4. DNone of these

Correct answer

A. y= 32 x 9

Step-by-step solution

The diameters y=m₁ x and y=m₂ x are conjugate diameters of the hyperbola x^2 a^2 - y^2 b^2 =1 , if m₁ m₂= b^2 a^2 Given equation is x^2 9 - y^2 16 =1 Here, a^2=9, b^2=16 Also given, x=2 y Then, m₁= 1 2 1 2 m₂= 16 9 m₂= 32 9 Hence, the required equation of diameter is y= 32 x 9

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