A) \[{{x}^{2}}+{{y}^{2}}=16\]
B) \[{{x}^{2}}+{{y}^{2}}=4\]
C) \[{{x}^{2}}+{{y}^{2}}=20\]
D) \[{{x}^{2}}+{{y}^{2}}=12\]
Correct Answer: D
Solution :
Equation of director circle of the parabola\[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{4}=1\] (where \[{{a}^{2}}=16,\,{{b}^{2}}=4\]) is \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}=16-4\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}=12\]
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