# The minimum distance between any two points and while considering point on one circle and point on the other circle for the given circles' equations  and  is ______________. Option: 1 1 Option: 2 2 Option: 3 3 Option: 4 4

$\\x^{2}+y^{2}-10 x-10 y+41=0 \\ (x-5)^2+(y-5)^2=3^2$

$C_1=(5,5)\qquad r_1=3$

$\\ x^{2}+y^{2}-24 x-10 y+160=0 \\ (x-12)^2+(y-5)^2=3^2$

$C_2=(12,5)\qquad r_1=3$

$\begin{array}{l} \text { Now, } C _{1} C _{2}> r _{1}+ r _{2} \\ \text { Thus, }\left( P _{1} P _{2}\right)_{\min }=7-6=1 \end{array}$

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