A) \[(4\sqrt{2},2\sqrt{3})\]
B) \[(4\sqrt{3},2\sqrt{3})\]
C) \[(4\sqrt{2},2\sqrt{2})\]
D) \[(4\sqrt{3},2\sqrt{2})\]
Correct Answer: D
Solution :
Let the equation of the ellipse is\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\therefore \]\[\frac{2{{b}^{2}}}{a}=8\Rightarrow {{b}^{2}}=4a\]and\[2ae=2b\Rightarrow e=\frac{b}{a}\] Since,\[{{e}^{2}}=1-\frac{{{b}^{2}}}{{{a}^{2}}}\] \[\Rightarrow \]\[{{e}^{2}}=1-{{e}^{2}}\]\[\Rightarrow \]\[e=\frac{1}{\sqrt{2}}\] Now,\[\frac{1}{2}=1-\frac{4a}{{{a}^{2}}}\Rightarrow a=8\]and\[b=ae=8.\frac{1}{\sqrt{2}}=4\sqrt{2}\] \[\therefore \] Equation of ellipse is\[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{32}=1\] The point only in option i.e., \[(4\sqrt{3},2\sqrt{2})\]lies on the ellipse.
You need to login to perform this action.
You will be redirected in
3 sec
