A) \[{{x}^{2}}+{{y}^{2}}-ax-by=0\]
B) \[{{x}^{2}}+{{y}^{2}}+ax+by=0\]
C) \[{{x}^{2}}+{{y}^{2}}-2ax-2by=0\]
D) None of these
Correct Answer: A
Solution :
\[\lambda (x-a)+(y-b)=0\]is the equation of line. \[r=-\left( \frac{-a\lambda -b}{{{\lambda }^{2}}+1} \right)\] Coordinates of point \[\equiv \left\{ -\lambda \left( \frac{-a\lambda -b}{{{\lambda }^{2}}+1} \right)\text{ },-\left( \frac{-a\lambda -b}{{{\lambda }^{2}}+1} \right) \right\}\] \[h=\lambda \left( \frac{a\lambda +b}{{{\lambda }^{2}}+1} \right)\text{ },k=\frac{a\lambda +b}{{{\lambda }^{2}}+1},\lambda =\frac{h}{k}\] \[\therefore h=h\left( \frac{ah+kb}{{{h}^{2}}+{{k}^{2}}} \right)\Rightarrow {{x}^{2}}+{{y}^{2}}=ax+by.\]
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