A) \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\]
B) \[{{x}^{2}}+{{y}^{2}}+x+y-1=0\]
C) \[{{x}^{2}}+{{y}^{2}}-2x-2y-1=0\]
D) None of these
Correct Answer: A
Solution :
The centre of given circle is (1, 1) and its radius is \[\sqrt{2}\]. From the figure, if \[M(h,\ k)\] be the middle point of chord AB subtending an angle \[\frac{2\pi }{3}\] at C, then \[\frac{CM}{AC}=\cos \frac{\pi }{3}=\frac{1}{2}\Rightarrow 4C{{M}^{2}}=A{{C}^{2}}\] or \[4[{{(h-1)}^{2}}+{{(k-1)}^{2}}]=4\Rightarrow {{h}^{2}}+{{k}^{2}}-2h-2k+2=1\] Hence the locus is\[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\].You need to login to perform this action.
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