A) 3
B) 2
C) 1
D) 5
E) 6
Correct Answer: A
Solution :
The equation of circles are \[{{(x-2)}^{2}}+{{(y-3)}^{2}}={{r}^{2}}\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}-4x-6y-{{r}^{2}}+13=0\] ...(i) and \[{{(x-5)}^{2}}+{{(y-6)}^{2}}={{r}^{2}}\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}-10x-12y-{{r}^{2}}+61=0\] ...(ii) The given circles cut orthogonally, if \[2.(-2)(-5)+2(-3)(-6)=\] \[-{{r}^{2}}+13-{{r}^{2}}+61\] \[\Rightarrow \]\[20+36-13-61=-2{{r}^{2}}\] \[\Rightarrow \] \[r=3\]You need to login to perform this action.
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