A) \[9{{x}^{2}}+4{{y}^{2}}=36\]
B) \[4{{x}^{2}}+9{{y}^{2}}=36\]
C) \[36{{x}^{2}}+9{{y}^{2}}=4\]
D) \[9{{x}^{2}}+36{{y}^{2}}=4\]
Correct Answer: B
Solution :
\[\because \,ae=\pm \sqrt{5}\] Þ \[a=\pm \sqrt{5}\left( \frac{3}{\sqrt{5}} \right)=\pm 3\] Þ \[{{a}^{2}}=9\] \\[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})=9\left( 1-\frac{5}{9} \right)=4\] Hence, equation of ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\]Þ \[4{{x}^{2}}+9{{y}^{2}}=36\].
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