Explanation:
B The equation of ellipse is given, \(9 \mathrm{x}^2+5 \mathrm{y}^2-30 \mathrm{y}=0\)
Now, adding 45 on both sides.
\(9 x^2+5 y^2-30 y+45=45\)
\(9 x^2+5\left(y^2-6 y+9\right)=45\)
\(9 x^2+5(y-3)^2=45\)
\(\frac{x^2}{5}+\frac{(y-3)^2}{9}=1\)
Which is the general equation of an ellipse here, \(\mathrm{a}^2=5, \mathrm{~b}^2=9\)
So, the eccentricity of the ellipse is,
\(\mathrm{e}=\sqrt{\frac{\mathrm{b}^2-\mathrm{a}^2}{\mathrm{~b}^2}}\)
\(\mathrm{e}=\sqrt{\frac{9-5}{9}}\)
\(\mathrm{e}=\sqrt{\frac{4}{9}}=\frac{2}{3}\)