Question

Distance between the directrices of the ellipse $9x^2+5y^2-30y=0$ is

• A. $\frac{9}{2}$
• B. $18$
• C. $9$
• D. $12$

Answer 1

Answer: (C)

$9$

$9x^2+5y^2-30y=0$
$\Rightarrow \frac{x^2}{5}+\frac{{(y-3)}^2}{9}=1$
$e=\sqrt{1-\frac{a^2}{b^2}}=\sqrt{1-\frac{5}{9}}=\frac{2}{3}$
It is a vertical ellipse
Therefore, distance between directrix is $\frac{2b}{e}=9$