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
$x^{2} + y^{2} - 10 x - 10 y + 41 = 0$
$x^{2} + y^{2} - 24 x - 10 y + 160 = 0$ is ________

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

$x^{2} + y^{2} - 10 x - 10 y + 41 = 0$

$x^{2} + y^{2} - 24 x - 10 y + 160 = 0$ is ________

Aicharya · Accepted Answer

Given C 1 ( 5 , 5 ) , &#160; r 1 = 3 and C 2 ( 12 , 5 ) , &#160; r 2 = 3 C 1 C 2 = 7 Now, C 1 C 2 &#62; r 1 + r 2 Thus, P 1 P 2 min = 7 - 6 = 1

The minimum distance between any two points P 1 and P 2 while considering point P 1 on one circle and point…

Solution