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A hyperbola having the transverse axis of length 2 units has the same focii as that of ellipse 3 x 2 + 4 y 2 = 12 , then its equation is

Options

  1. A2 x 2 - 2 y 2 = 1
  2. B2 x 2 - 2 y 2 = 3
  3. Cx 2 - y 2 = - 2
  4. Dx 2 - y 2 = 2

Correct answer

A. 2 x 2 - 2 y 2 = 1

Step-by-step solution

For the hyperbola x 2 a 2 - y 2 b 2 = 1 , length of semi transverse axis a = 1 2 , For the ellipse x 2 4 + y 2 3 = 1 , the foci is ± 1,0 i.e. ± 1 = ± a 2 + b 2 ⇒ b 2 = 1 - a 2 = 1 - 1 2 = 1 2   Hence, the equation of the required hyperbola is x 2 1 2 - y 2 1 2 = 1

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