Question

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

• A. 8
• B. 12
• C. 18
• D. 24

Answer 1

The correct option is C

18

a = 6 , b = $2\sqrt{5}$

$b^2=a^2(1-e^2)\Rightarrow \frac{20}{36}=(1-e^2)\Rightarrow e=\sqrt{\frac{16}{36}}=\frac{2}{3}$

But directrices are x = $\pm \frac{a}{e}$

Hence distance between them is $2.\frac{6}{\frac{2}{3}}=18.$