Question

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

• A. 3/5
  
• B. 1/3
  
  
• C. 2/5
  
  
• D. 1/5

Answer 1

The correct option is A 3/5


$25x^2+16y^2=400$
$\Rightarrow \frac{x^2}{16}+frac{y}^{2}25=1$ ...(1)
Comparing equation (1) is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, we get:
$a^2=16$ and $b^2=25$
Here, a<b, so the major and the minor axes of the ellipse are along the x-axis and y-axis, respectively.
Now, $e=\sqrt{1-\frac{b^2}{a^2}}$
$\Rightarrow e=\sqrt{1-\frac{16}{25}}$
$\Rightarrow e=\sqrt{\frac{9}{25}}$
$\Rightarrow e=\frac{3}{5}$