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The equation of the hyperbola with vertices 3 , 0 , − 3 , 0 and semi-latus rectum 4 is given by:

Options

  1. A4 x 2 - 3 y 2 + 36 = 0
  2. B4 x 2 - 3 y 2 + 12 = 0
  3. C4 x 2 - 3 y 2 - 36 = 0
  4. D4 x 2 + 3 y 2 - 25 = 0

Correct answer

C. 4 x 2 - 3 y 2 - 36 = 0

Step-by-step solution

We have a = 3 and b 2 a = 4 ⇒ b 2 = 12 Hence, the equation of the hyperbola is x 2 9 − y 2 12 = 1 ⇒ 4 x 2 − 3 y 2 = 36 ⇒   4 x 2 − 3 y 2 − 36 = 0

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