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The minimum distance between any two points P_1 and P_2 while considering point P_1 on one circle and point P_2 on the other circle for the given circles' equations x^{2}+y^{2}-10x-10y+41=0 and x^{2}+y^{2}-24x-10y+160=0 is ______________.
Option: 1 1
Option: 2 2
Option: 3 3
Option: 4 4

Answers (1)

best_answer

\\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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Suraj Bhandari

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