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Manipal MET2010MathematicsHyperbola

If the equation l x^2+2 m x y+n y^2=0 represents a pair conjugate diameter of the hyperbola x^2 a^2 - y^2 b^2 =1 , then

Options

  1. Al a^2+n b^2=0
  2. Bl a^2=n b^2
  3. C2 l a^2=n b^2
  4. DNone of these

Correct answer

B. l a^2=n b^2

Step-by-step solution

Let y=m₁ x and y=m₂ x be the lines represented by l x^2+2 m x y+n y^2=0 , then m₁ m₂= l n ...(i) But y=m₁ x and y=m₂ x are conjugate diameters of the hyperbola. m₁ m₂= b^2 a^2 ...(ii) From Eqs. (i) and (ii), we get l n = b^2 a^2 l a^2=n b^2

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