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Grade 12th passAnalytical Geometry

If e and e' are eccentricity of a hyperbola and its conjucate, then state whether ee' >1 is true or false with reason?

Profile image of Pawan joshi
7 Years agoGrade 12th pass
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2 Answers

Profile image of Arun
7 Years ago
Dear student
 
e^2 = 1 + b^2 /a^2 = (a^2 + b^2) / a^2
 
hence
(e’)^2 = (a^2 + b^2) / b^2
 
hence when multiplying
 
(e e’)^2 = (a^2 + b^2) ^2 / a^2 b^2
 
now use AM GM and you will find that
 
ratio os greater than one
 
Profile image of Arun
7 Years ago
Dear student
 
You can also tell because
 
hyperbola has eccentricity greater than 1.
 
hence, whether it is conjugate hyperbola or hyperbola , eccentricity will always be 1.
 
hence 
 
e> 1 , e’ > 1
 
e e’ > 1

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