Question

The eccentricity of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is:

• A. $\frac{\sqrt{5}}{2}$
• B. $\frac{2}{3}$
• C. $\frac{\sqrt{5}}{3}$
• D. $\frac{4}{9}$

Answer 1

Answer: (C)

$\frac{\sqrt{5}}{3}$

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

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

$\therefore e=\sqrt{1-\frac{a^2}{b^2}}=\sqrt{1-\frac{4}{9}}=\frac{\sqrt{5}}{3}$