Question

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

• A. $\frac{2\sqrt{5}}{4}$
• B. $\frac{2\sqrt{13}}{6}$
• C. $\frac{2\sqrt{5}}{6}$
• D. $\frac{2\sqrt{13}}{14}$

Answer 1

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

$\frac{x^2}{36}+\frac{y^2}{16}=1$
$\frac{x^2}{6^2}+\frac{y^2}{4^2}=1$
$a=6,b=4$
$e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{4^2}{6^2}}$
$e=\sqrt{1-\frac{16}{36}}=\sqrt{\frac{20}{36}}$
$e=\frac{2\sqrt{5}}{6}$