A) \[{{g}^{2}}+{{f}^{2}}=3c\]
B) \[{{g}^{2}}+{{f}^{2}}=2c\]
C) \[{{g}^{2}}+{{f}^{2}}=5c\]
D) \[{{g}^{2}}+{{f}^{2}}=4c\]
Correct Answer: B
Solution :
Clearly, (0, 0) lies on director circle of the given circle. Now, equation of director circle is, \[{{(x+g)}^{2}}+{{(y+f)}^{2}}=2({{g}^{2}}+{{f}^{2}}-c)\] It (0, 0) lies on it, then \[{{g}^{2}}+{{f}^{2}}=2({{g}^{2}}+{{f}^{2}}-c)\] \[\Rightarrow \] \[{{g}^{2}}+{{f}^{2}}=2c\]
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