A) \[{{x}^{2}}+2{{y}^{2}}=100\]
B) \[{{x}^{2}}+\sqrt{2}{{y}^{2}}=10\]
C) \[{{x}^{2}}-2{{y}^{2}}=100\]
D) None of these
Correct Answer: A
Solution :
Given \[\frac{2{{b}^{2}}}{a}=10\] and \[2b=2ae\] Also \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] Þ \[{{e}^{2}}=(1-{{e}^{2}})\] Þ \[e=\frac{1}{\sqrt{2}}\] Þ \[b=\frac{a}{\sqrt{2}}\] or\[b=5\sqrt{2}\], \[a=10\] Hence equation of ellipse is \[\frac{{{x}^{2}}}{{{(10)}^{2}}}+\frac{{{y}^{2}}}{{{(5\sqrt{2})}^{2}}}=1\] i.e., \[{{x}^{2}}+2{{y}^{2}}=100\].
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