A) \[\left( \pm \frac{5}{\sqrt{6}},\ 0 \right)\]
B) \[\left( \pm \frac{5}{6},\ 0 \right)\]
C) \[\left( \pm \frac{\sqrt{5}}{6},\ 0 \right)\]
D) None of these
Correct Answer: A
Solution :
The given equation is \[2{{x}^{2}}-3{{y}^{2}}=5\] \[\Rightarrow \,\]\[\frac{{{x}^{2}}}{5/2}-\frac{{{y}^{2}}}{5/3}=1\] Now \[{{b}^{2}}={{a}^{2}}({{e}^{2}}-1)\]\[\Rightarrow \,\frac{5}{3}=\frac{5}{2}({{e}^{2}}-1)\] Þ \[e=\sqrt{\frac{5}{3}}\]. The foci of hyperbola \[(\pm \,ae,\,0)\] \[=\left( \pm \sqrt{\frac{5}{2}}\,.\,\sqrt{\frac{5}{3}},0 \right)\]\[=\left( \pm \,\frac{5}{\sqrt{6}},0 \right)\].
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