Question

The eccentricity of the ellipse $5x^2+9y^2=1$ is

• A. 2/3
  
• B. 3/4
  
• C. 4/5
  
• D. 1/2

Answer 1

The correct option is A 2/3


$5x^2+9y^2=1$
$\Rightarrow \frac{x^2}{5}+\frac{y^2}{9}=1$
$\therefore a=\sqrt{5}$ and b=3
Here, b>a so the major and the minor axes of the ellipse are along the x-axis and y-axis, respectively.
Now, $e=\sqrt{1-\frac{a^2}{b^2}}$
$\Rightarrow e=\sqrt{1-\frac{5}{9}}$
$\Rightarrow e=\sqrt{\frac{4}{9}}$
$\Rightarrow e=\frac{2}{3}$