The eccentricity of the ellipse 9 x^2 + 5 y^2 - 30y = 0, is - Vidyadip

MCQ

The eccentricity of the ellipse $9{x^2} + 5{y^2} - 30y = 0$, is

A
$1\over3$
✓
$2\over3$
C
$3\over4$
D
None of these

✓

Answer

Correct option: B.

$2\over3$

b
(b) $9{x^2} + {(\sqrt 5 y - 3\sqrt 5 )^2} = 45$ or $\frac{{{x^2}}}{5} + \frac{{{{(y - 3)}^2}}}{9} = 0$

==> ${a^2} = 5,$ ${b^2} = 9$.

Therefore $e = \frac{2}{3}$.

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