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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.

 Mar 20, 2020
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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

 Mar 20, 2020

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