Mathematics - Ellipse Question with Solution | TestHub

Given, $2ae=6$ and $\frac{2a}{e}=12$, directrices are $x=\pm \frac{a}{e}$

So, $\frac{a}{e}=6$

Now, using the formula for eccentricity of an ellipse

$\Rightarrow b^2=a^2-a^2{e}^2=18-9=9$

$\Rightarrow L.R.=\frac{2b^2}{a}=\frac{2\times 9}{3\sqrt{2}}=3\sqrt{2}$