Question 11 Mark
Find the eccentricity of the hyperbola $9y^2 - 4x^2 = 36.$
Answer
View full question & 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 $\text{a}^2=\text{b}^2(\text{e}^2-1)$
$\therefore\ 9=4(\text{e}^2-1)$
$\Rightarrow\text{e}=\sqrt{1+\frac{9}{4}}$
$\Rightarrow\text{e}=\frac{\sqrt{13}}{2}$
$=-1$ We kanow that $\text{a}^2=\text{b}^2(\text{e}^2-1)$
$\therefore\ 9=4(\text{e}^2-1)$
$\Rightarrow\text{e}=\sqrt{1+\frac{9}{4}}$
$\Rightarrow\text{e}=\frac{\sqrt{13}}{2}$