What is the shortest distance, in units, between the circles $(x-9)^2 + (y-5)^2 = 6.25$ and $(x+6)^2 + (y+3)^2 = 49$? Express your answer as a decimal to the nearest tenth.
+23245 My plan is to find the distance between the centers of the two circles and subtract the lengths of the radii of the two circles.
(x - 9)2 + (y - 5)2 = 6.25 ---> C(9,5) r = 2.5
(x + 6)2 + (y + 3)2 = 49 ---> C(-6,-3) r = 7
Distance between (9,5) and (-6,-3) = sqrt[ (-6 - 9)2 + (-3 - 5)2 ] = sqrt[ (-15)2 + (-8)2 ]
= sqrt( 225 + 64) = sqrt(289) = 17
Distacne between the two circles: 17 - 2.5 - 7 = 7.5
