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KCET2013MathematicsHyperbola

If the distance between the focii and the distance between the directrices of the hyperbola x² a² - y² b² =1 are in the ratio 3: 2 , then a: b is

Options

  1. A2 : 1
  2. B1: 2
  3. C3 : 2
  4. D2: 1

Correct answer

A. 2 : 1

Step-by-step solution

Given equation of hyperbola is x² a² - y² b² =1 Now, distance between the focii =2 a e and distance between the directrices = 2 a e (by condition) Given, ratio =3: 2 2 a e (2 a / e) = 3 2 4 a e²=6 a e²= 3 2 e= 3 2 ...(i) Eccentricity of hyperbola = a²+b² a² a²+b² a² = 3 2 [from Eq. (i)] a²+b² a² = 3 2 (squaring on both sides) 1+ b² a² = 3 2 ( b a )²= 1 2 b a = 1 2 Hence, a: b= 2 : 1

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