A) \[{{x}^{2}}+{{y}^{2}}-x{{x}_{1}}-y{{y}_{1}}=0\]
B) \[{{x}^{2}}+{{y}^{2}}=x_{1}^{2}+y_{1}^{2}\]
C) \[x+y={{x}_{1}}+{{y}_{1}}\]
D) \[x+y=x_{1}^{2}+y_{1}^{2}\]
E) \[{{x}^{2}}-{{y}^{2}}-x_{1}^{2}-y_{1}^{2}=0\]
Correct Answer: A
Solution :
Let\[p({{x}_{1}},{{y}_{1}})\]be the point, then the chord of contact of tangents drawn from P to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]is \[x{{x}_{1}}+y{{y}_{1}}={{a}^{2}}\] \[\therefore \] \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\left( \frac{x{{x}_{1}}+y{{y}_{1}}}{{{a}^{2}}} \right)\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-x{{x}_{1}}-y{{y}_{1}}=0\] Which is required equation.
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