Find the eccentricity of the hyperbola 9y^2 - 4x^2 = 36. - Vidyadip

Question

Find the eccentricity of the hyperbola $9y^2 - 4x^2 = 36.$

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Answer

We have the hyperbola $9y^2 - 4x^2 = 36$ Or $\frac{\text{x}^2}{9}-\frac{\text{y}^2}{4}$
$=-1$ We kanow that $\text{a}^2=\text{b}^2(\text{e}^2-1)$
$\therefore\ 9=4(\text{e}^2-1)$
$\Rightarrow\text{e}=\sqrt{1+\frac{9}{4}}$
$\Rightarrow\text{e}=\frac{\sqrt{13}}{2}$

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