A) 1/3
B) 2/3
C) 3/4
D) none of these
Correct Answer: B
Solution :
Given equation of ellipse is \[9{{x}^{2}}+5{{y}^{2}}-30y=0\] or \[9{{x}^{2}}+5({{y}^{2}}-6y+9)=45\] or \[\frac{{{x}^{2}}}{5}+\frac{{{(y-3)}^{2}}}{9}=1\] On comparing with\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] Here, \[{{a}^{2}}=5,\,{{b}^{2}}=9\] \[\therefore \] Eccentricity,\[e=\sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}\] \[(\because \,b>a)\] \[=\sqrt{1-\frac{5}{9}}=\frac{2}{3}\] Note: Eccentricity of ellipse is lying between 0 to 1.
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