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Let the eccentricity of the hyperbola with the principal axes along the coordinate axes and passing through 3,0 and 3 2 , 2 is e , then the value of e 2 + 1 e 2 - 1 is equal to

Correct answer

5.5

Step-by-step solution

One vertex of the hyperbola is 3,0 . So, assuming the equation of hyperbola as x 2 9 - y 2 b 2 = 1 and passing through 3 2 , 2 , we get, ⇒ 9 2 9 - 4 b 2 = 1 ⇒ 1 = 4 b 2 ⇒ b 2 = 4 ⇒ e 2 = 1 + b 2 a 2 = 1 + 4 9 = 13 9 ⇒ e 2 + 1 e 2 - 1 = 13 9 + 1 13 9 - 1 = 22 4 = 11 2 = 5 . 5

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