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


$5x^2+9y^2=1$
$\Rightarrow \frac{x^2}{\frac{1}{6}}+\frac{y^2}{\frac{1}{9}}=1$
Comparing with the standard equation of the ellipse, we get:
$a^2=\frac{1}{5}$ and $b^2=\frac{1}{9}$
i.e., $a=\frac{1}{\sqrt{5}}$ and $b=\frac{1}{3}$
Here, a>b
Now, $e=\sqrt{1-\frac{b^2}{a^2}}$
$\Rightarrow e=\sqrt{1-\frac{\frac{1}{9}}{\frac{1}{5}}}$
$\Rightarrow e=\sqrt{1-\frac{5}{9}}$
$\Rightarrow e=\sqrt{\frac{4}{9}}$
$\Rightarrow e=\frac{2}{3}$