Question

The eccentricity of the ellipse $\frac{x^2}{225}+\frac{y^2}{289}=1$ is:

• A. $\frac{17}{8}$
• B. $\frac{8}{17}$
• C. $\frac{3}{4}$
• D. $\frac{4}{3}$

Answer 1

The correct option is B $\frac{8}{17}$

The equation of the ellipse is $\frac{x^2}{225}+\frac{y^2}{289}=1.$

We also know that the standard equation of the ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1.$

Comparing the given equation with the standard equation, we get $a^2=225,b^2=289.$

We also know that the relation for the eccentricity of an ellipse $\left(e\right),$ when $b>a,$ is $e^2=\frac{b^2-a^2}{b^2}=\frac{289-225}{289}=\frac{64}{289}\Rightarrow e=\frac{8}{17}.$