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 conditions, \[2ae=2.2a\] or \[\sqrt{{{(x-2)}^{2}}+{{y}^{2}}}=4-\sqrt{{{(x-2)}^{2}}+{{y}^{2}}}\]and\[A\equiv (0,\,0);\,B\equiv (4a,\,4a)\]. Hence, \[a=\frac{3}{\sqrt{3}}=\sqrt{3}\] Therefore, equation is \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{9}=1\]i.e., \[3{{x}^{2}}-{{y}^{2}}=9\].
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