A) \[\frac{{{x}^{2}}}{{{3}^{2}}}+\frac{{{y}^{2}}}{{{5}^{2}}}=1\]
B) \[\frac{{{x}^{2}}}{{{5}^{2}}}+\frac{{{y}^{2}}}{{{3}^{2}}}=1\]
C) \[\frac{{{x}^{2}}}{{{5}^{2}}}+\frac{{{y}^{2}}}{{{4}^{2}}}=1\]
D) \[\frac{{{x}^{2}}}{{{4}^{2}}}+\frac{{{y}^{2}}}{{{5}^{2}}}=1\]
Correct Answer: B
Solution :
Here \[ae=4\]and\[e=\frac{4}{5}\Rightarrow a=5\] Now \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\Rightarrow {{b}^{2}}=25\left( 1-\frac{16}{25} \right)=9\] Hence equation of the ellipse is \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{9}=1\].
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