Question

The eccentricity of an ellipse $9x^2+16y^2=144$ is

• A. $\frac{\sqrt{7}}{4}$
• B. $\frac{2}{5}$
• C. $\frac{\sqrt{3}}{5}$
• D. $\frac{\sqrt{5}}{3}$

Answer 1

The correct option is A $\frac{\sqrt{7}}{4}$

The general equation of the ellipse is,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
The eccentricity of the ellipse is,
$e=\sqrt{1-\frac{b^2}{a^2}}$
Given ellipse is,
$\frac{x^2}{16}+\frac{y^2}{9}=1$
Therefore, eccentricity is
$e=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4}$