A) \[\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{16}=1\]
B) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1\]
C) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{8}=1\]
D) None of these
Correct Answer: B
Solution :
The foci of an ellipse \[\frac{{{x}^{2}}}{{{\alpha }^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is given by\[(\pm \,ae,\,\,0)\]. Since, \[e=\frac{1}{2},\,\,ae=2\] \[\Rightarrow \] \[a=4\] \[\therefore \] \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})-16\left( 1-\frac{1}{4} \right)=12\] Hence, the equation of an ellipse is \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1\]
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