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If e and e' are eccentricities of a hyperbola and it's conjugate, then find the value of .

  1. 2
  2. 0
  3. -1
  4. 1

Answer (Detailed Solution Below)

Option 4 : 1
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Detailed Solution

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Concept:

Hyperbola:

  • The general equation of a hyperbola is  and its conjugate hyperbola is .
  • The eccentricity e of the hyperbola  is given by e =  (more than 1).


Calculation:

Let the equation of the hyperbola be .

∴ The equation of its conjugate hyperbola will be  or .

Now, the eccentricity of the hyperbola, e = .

⇒ e2 = .

Also, eccentricity of the conjugate hyperbola will be e' = .

⇒ e'2 = .

Finally,  = 1.

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