A) (0, 0)
B) (1, 1)
C) (1, -1)
D) (-1, -1)
Correct Answer: B
Solution :
\[{{x}^{2}}+{{y}^{2}}-6x-6y+10=0\] ?. (i) \[{{x}^{2}}+{{y}^{2}}=2\] ?. (ii) \[\Rightarrow -6x-6y+12=0\] or \[x+y-2=0\] ?. (iii) \[\Rightarrow {{x}^{2}}+{{y}^{2}}+2xy=4\] {from (iii)} or \[2xy=2\] {from (ii)} and \[x-y=\sqrt{{{(x+y)}^{2}}-4xy}=\sqrt{4-4}=0\] or \[x=y\] and \[x+y=2\]\[\Rightarrow x=1,\ y=1\]. Trick: Required point must satisfy both the circles. Obviously (1, 1) satisfies both the equations simultaneously.
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