Question

The eccentricity of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$ is

• A. $\frac{2\sqrt{5}}{6}$
• B. $\frac{2\sqrt{5}}{4}$
• C. $\frac{2\sqrt{13}}{6}$
• D. $\frac{2\sqrt{13}}{4}$

Answer 1

The correct option is A $\frac{2\sqrt{5}}{6}$

The eccentricity of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$ is given by
$e^2=1-\frac{b^2}{a^2}$
Using the formula
$e^2=1-\frac{16}{36}=\frac{5}{9}\Rightarrow e=\frac{\sqrt{5}}{3}=\frac{2\sqrt{5}}{6}$