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The equation of the hyperbola having eccentricity 2 , such that the distance between its foci is 8 and the major axis is along the x -axis, while the minor axis is along the   y -axis, is

Options

  1. Ax 2 12 - y 2 4 = 1
  2. Bx 2 4 - y 2 12 = 1
  3. Cx 2 8 - y 2 2 = 1
  4. Dx 2 16 - y 2 9 = 1

Correct answer

B. x 2 4 - y 2 12 = 1

Step-by-step solution

Distance between foci = 8 = 2 a e But e = 2 . Therefore, 2 a = 4 ⇒ a = 2 ⇒ a 2 = 4 And b 2 = a 2 e 2 - 1 = 4 4 - 1 = 12 ∴ Equation of hyperbola is x 2 4 - y 2 12 = 1

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