A) \[\frac{13}{3}\]
B) \[\sqrt{13}\]
C) \[\sqrt{3}\]
D) \[\frac{\sqrt{13}}{3}\]
E) \[\frac{5}{3}\]
Correct Answer: D
Solution :
\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}}=1\]pass through (3, 0) and\[(3\sqrt{2},2)\] \[\therefore \] \[\frac{9}{{{a}^{2}}}=1\Rightarrow {{a}^{2}}=9\] and \[\frac{9\times 2}{9}-\frac{4}{{{b}^{2}}}=1\] \[\Rightarrow \] \[2-1=\frac{4}{{{b}^{2}}}\]\[\Rightarrow \]\[{{b}^{2}}=4\] \[\therefore \] \[e=\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}}=\sqrt{1+\frac{4}{9}}=\frac{\sqrt{13}}{3}\]
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