A) \[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1\]
B) \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{3}=1\]
C) \[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=\frac{4}{3}\]
D) None of these
Correct Answer: B
Solution :
Given that, \[e=\frac{1}{2}\] and \[(\pm \,ae,\,0)=\,(\pm \,1,\,0)\] \[\Rightarrow \,ae=1\] \[\Rightarrow a=2\]. Now \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] \[\Rightarrow \,\,\,{{b}^{2}}=4\left( 1-\frac{1}{4} \right)\]\[\Rightarrow \,\,{{b}^{2}}=3\] Hence, equation of ellipse is \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{3}=1.\]
You need to login to perform this action.
You will be redirected in
3 sec
