Question

The eccentricity of the ellipse $25x^2+16y^2=400$ is

• A. $\frac{3}{5}$
• B. $\frac{1}{3}$
• C. $\frac{1}{5}$
• D. $\frac{2}{5}$

Answer 1

The correct option is A $\frac{3}{5}$

Given: Equation of ellipse, $25x^2+16y^2=400$

$\Rightarrow \frac{x^2}{16}+\frac{y^2}{25}=1$

On comparing with standard form: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

We get, $a^2=16\text{and}{b}^2=25$

Eccentricity,

$e=\sqrt{1-\frac{a^2}{b^2}}[\because b>a]$

$\Rightarrow e=\sqrt{1-\frac{16}{25}}$

$\Rightarrow e=\sqrt{\frac{9}{25}}$

$\therefore e=\frac{3}{5}[\because e>0]$

Hence, option (A) is correct.