A) \[3{{x}^{2}}+4{{y}^{2}}=48\]
B) \[4{{x}^{2}}+3{{y}^{2}}=48\]
C) \[3{{x}^{2}}+4{{y}^{2}}=0\]
D) \[4{{x}^{2}}+3{{y}^{2}}=0\]
Correct Answer: A
Solution :
Since, \[ae=\pm \,2\] \[\Rightarrow \,a=\pm \,4\] \[(\because \,\,e=1/2)\] Now \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\]\[\Rightarrow \]\[{{b}^{2}}=16(1-1/4)\]\[\Rightarrow \]\[{{b}^{2}}=12\] Hence ellipse is\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1\]\[\Rightarrow \]\[3{{x}^{2}}+4{{y}^{2}}=48\].
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