Question

The eccentricity of the ellipse $4x^2+9y^2=36$

• A. $\frac{1}{2\sqrt{3}}$
  
• B. $\frac{1}{\sqrt{3}}$
  
• C. $\frac{\sqrt{5}}{3}$
  
• D. $\frac{\sqrt{5}}{6}$

Answer 1

The correct option is C $\frac{\sqrt{5}}{3}$


$4x^2+9y^2=36$
$\Rightarrow \frac{x^2}{9}+\frac{y^2}{4}=1$
Comparing it with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, we get:
a=3 and b=2
Here, a>b so the major and the minor axes of the ellipse are along the x-axis and y-axis, respectively.
Now, $e=\sqrt{1-\frac{b^2}{a^2}}$
$\Rightarrow e=\sqrt{1-\frac{4}{9}}$
$\Rightarrow e=\sqrt{\frac{5}{9}}$
$\Rightarrow e=\frac{\sqrt{5}}{3}$.