Question

The eccentricity of the ellipse $12x^2+7y^2=84$ is equal to :

• A. $\frac{\sqrt{5}}{7}$
• B. $\sqrt{\frac{5}{7}}$
• C. $\frac{\sqrt{5}}{12}$
• D. $\frac{5}{7}$
• E. $\frac{7}{12}$

Answer 1

The correct option is B $\sqrt{\frac{5}{7}}$

Given equation is $12x^2+7y^2=84$

It can be rewritten as
$\frac{x^2}{84/12}+\frac{y^2}{84/7}=1$
$\Rightarrow \frac{x^2}{7}+\frac{y^2}{12}=1$
Here, $a^2=7,b^2=12$ i.e., $b>a$
Therefore, $e=\sqrt{1-\frac{a^2}{b^2}}$

$=\sqrt{1-\frac{7}{12}}$
$=\sqrt{\frac{5}{12}}$