A) \[\frac{{{x}^{2}}}{18}+\frac{{{y}^{2}}}{32}=1\]
B) \[\frac{{{x}^{2}}}{8}+\frac{{{y}^{2}}}{9}=1\]
C) \[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{32}=1\]
D) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{24}=1\]
Correct Answer: C
Solution :
\[\frac{2{{b}^{2}}}{a}=8,\]\[e=\frac{1}{\sqrt{2}}\]Þ \[{{a}^{2}}=64,\,{{b}^{2}}=32\] Hence required equation of ellipse is\[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{32}=1\].
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