Question

Find the eccentricity of the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$.

Answer 1

Given the equation of the ellipse is $\frac{x^2}{9}+\frac{y^2}{5}=1$.

Comparing this with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ we get, $a^2=9,b^2=3$.

The eccentricity of the ellipse is $\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{5}{9}}=\frac{2}{3}$.