A) \[3{{x}^{2}}-{{y}^{2}}=3\]
B) \[{{x}^{2}}-3{{y}^{2}}=3\]
C) \[3{{x}^{2}}-{{y}^{2}}=9\]
D) \[{{x}^{2}}-3{{y}^{2}}=9\]
Correct Answer: C
Solution :
According to given condition,\[2ae=2\cdot 2a\] \[\Rightarrow \] \[e=2\] and \[2b=6\,\,\,\Rightarrow \,\,\,b=3\] Hence, \[a=\frac{3}{\sqrt{3}}=\sqrt{3}\] \[\therefore \]Required equation is \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{9}=1\] \[\Rightarrow \,\,\,3{{x}^{2}}-{{y}^{2}}=9\]
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