A) \[{{g}^{2}}+{{f}^{2}}=2c\]
B) \[g=f={{c}^{2}}\]
C) \[g+f=c\]
D) None of these
Correct Answer: A
Solution :
The equation of tangents will be \[c({{x}^{2}}+{{y}^{2}}+2gx+2fy+c)={{(gx+fy+c)}^{2}}\] These tangents are perpendicular, hence the coefficients of \[{{x}^{2}}\]+ coefficients of \[{{y}^{2}}=0\] \[\Rightarrow c-{{g}^{2}}+c-{{f}^{2}}=0\Rightarrow {{f}^{2}}+{{g}^{2}}=2c\].
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