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AP EAMCET2007MathematicsHyperbola

If the line l x+m y=1 is a normal to the hyperbola x^2 a^2 - y^2 b^2 =1 , then a^2 l^2 - b^2 m^2 is equal to

Options

  1. Aa^2-b^2
  2. Ba^2+b^2
  3. C(a^2+b^2 )^2
  4. D(a^2-b^2 )^2

Correct answer

C. (a^2+b^2 )^2

Step-by-step solution

If l x+m y+n=0 is normal to the hyperbola x^2 a^2 - y^2 b^2 =1 Then a^2 l^2 - b^2 m^2 = (a^2+b^2 )^2 n^2 Here, n=-1 , therefore a^2 l^2 - b^2 m^2 = (a^2+b^2 )^2 .

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