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

$\frac{9}{2}$

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Solution

The correct option is C
9

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

$\Rightarrow 9 x^{2} + 5 (y^{2} - 6 y + 9)$ = 45

$\Rightarrow \frac{x^{2}}{5} + \frac{(y - 3)^{2}}{9}$ = 1, e = $\sqrt{1 - \frac{5}{9}}$ = $\frac{2}{3}$

The distance between the two directrices = $\frac{2 b}{e}$ = $2 \times \frac{3}{\frac{2}{3}}$ = 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

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