Find the eccentricity of the hyperbola y²/4 - x²/9 = 1 ?

Correct Answer is : 132{{13}}{2}213

Correct Answer is : 132{{13}}{2}213

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UPSC NDA Math Model Paper 4

Question : 60 of 120

Marks: +1, -0

\frac{y^2}{4} - \frac{x^2}{9} = 1

Solution:

Given: Equation of hyperbola is

\frac{y^2}{4} - \frac{x^2}{9} = 1

As we know that, equation of vertical hyperbola is given by

\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1

So, by comparing the given equation of hyperbola with

\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1

we get,

\Rightarrow a^2 = 4

and

b^2 = 9

As we know that, eccentricity of a vertical hyperbola is given by

e = \frac{\sqrt{a^2+b^2}}{a}

So, the eccentricity of given hyperbola is

e = \frac{\sqrt{4+9}}{2} = \frac{\sqrt{13}}{2}

Hence, option B is the correct answer

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