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

\frac{9}{2}

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18

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9

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12

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Solution

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

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Similar questions

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

9 x^{2} + 5 y^{2} - 30 y = 0

9 x^{2} + 5 y^{2} = 30 y

9 x^{2} + 5 y^{2} - 30 y = 0

9 x^{2} + 5 y^{2} - 30 y = 0

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