Question

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

Answer 1

Given: $9y^2-4x^2=36$.

Dividing both sides by $36$, we get

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

It is vertical hyperbola i.e. , $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

$\Rightarrow a^2=4$ and $b^2=9$

We know that, $b^2=a^2(e^2-1)$

$\Rightarrow \frac{9}{4}=e^2-1$

$\Rightarrow e^2=\frac{13}{4}$

$\Rightarrow e=\frac{\sqrt{13}}{4}$

$\Rightarrow e=\frac{\sqrt{13}}{2}$

Hence, eccentricity of given hyperbola is $\frac{\sqrt{13}}{2}$