Question

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

• A. $\frac{\sqrt{11}}{3}$
• B. $\frac{\sqrt{15}}{3}$
• C. $\frac{\sqrt{13}}{3}$
• D. $\frac{\sqrt{14}}{3}$

Answer 1

Answer: (C)

$\frac{\sqrt{13}}{3}$

Given equation can be written as
$\frac{x^2}{9}-\frac{y^2}{4}=1$
Here $a=3,b=2$
$\therefore$ Eccentricity, $e=\sqrt{\frac{a^2+b^2}{a^2}}$
$=\sqrt{\frac{9+4}{9}}$
$=\sqrt{\frac{13}{9}}=\frac{\sqrt{13}}{3}$