Question

The distance between the directrices of the ellipse $\frac{x^2}{36}+\frac{y^2}{20}=1$ is ___________.

Answer 1

Given ellipse is of the form,
$\frac{x^2}{36}+\frac{y^2}{20}=1$
i.e a² = 36 and b² = 20
$$\begin{gathered} \therefore e=\sqrt{1-\frac{20}{36}} \\ =\sqrt{\frac{36-20}{36}} \\ =\sqrt{\frac{16}{36}} \\ e=\frac{4}{6}=\frac{2}{3} \end{gathered}$$
∴ equation of directrices is $x=\frac{a}{e}$ and $x=-\frac{a}{e}$
i.e $x=\frac{6}{2}\times 3\mathrm{and}x=-9$
i.e x = 9 and x = $-$9 are equations of directrices
$\therefore$ Distance between directrices is 18