A) \[\frac{1}{2}\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{\sqrt{{{g}^{2}}+{{f}^{2}}}} \right)\]
B) \[\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{\sqrt{{{g}^{2}}+{{f}^{2}}}} \right)\]
C) \[\frac{1}{2}\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{{{g}^{2}}+{{f}^{2}}} \right)\]
D) None of these
Correct Answer: A
Solution :
Chord of contact from origin \[\equiv gx+fy+c=0\] and from \[(g,\ f)\equiv gx+fy+g(x+g)+f(y+f)+c=0\] or \[2gx+2fy+{{g}^{2}}+{{f}^{2}}+c=0\] \[\therefore \] Distance\[=\frac{\frac{{{g}^{2}}+{{f}^{2}}+c}{2}-c}{\sqrt{{{g}^{2}}+{{f}^{2}}}}\]\[=\frac{{{g}^{2}}+{{f}^{2}}-c}{2\sqrt{{{g}^{2}}+{{f}^{2}}}}\].
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