Question:
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
\(x^2 + y^2 - 10x - 10y + 41 = 0\)
\(x^2 + y^2 - 24x - 10y + 160 = 0\) is ___________.
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
\(x^2 + y^2 - 10x - 10y + 41 = 0\)
\(x^2 + y^2 - 24x - 10y + 160 = 0\) is ___________.
\(x^2 + y^2 - 10x - 10y + 41 = 0\)
\(x^2 + y^2 - 24x - 10y + 160 = 0\) is ___________.
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For two separate circles, the minimum distance is (distance between centres) minus (sum of radii).
Updated On: Nov 4, 2026
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Correct Answer: 1
Solution and Explanation
Circle 1: centre \((5,5)\), \(r_1 = \sqrt{25 + 25 - 41} = 3\).
Circle 2: centre \((12,5)\), \(r_2 = \sqrt{144 + 25 - 160} = 3\).
Distance between centres \(= 7 > r_1 + r_2 = 6\), so the circles are separate (external).
Minimum distance \(= 7 - (3 + 3) = 1\).
Answer: 1
Circle 2: centre \((12,5)\), \(r_2 = \sqrt{144 + 25 - 160} = 3\).
Distance between centres \(= 7 > r_1 + r_2 = 6\), so the circles are separate (external).
Minimum distance \(= 7 - (3 + 3) = 1\).
Answer: 1
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