Two circles have the following equations: #(x +3 )^2+(y -5 )^2= 64 # and #(x -7 )^2+(y +2 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

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Answer 1 · 2017-03-21T07:26:14

The circles overlap and the greatest distance is #=29.2#

The centers of the circle are #(-3,5)# and #(7,-2)#

The distance between the centers is

#=sqrt((7+3)^2+(-2-5)^2)#

#=sqrt(10^2+7^2)#

#=sqrt(100+49)#

#=sqrt149=12.21#

The radii of the circles are #8# and #9#

The sum of the radii #=8+9=17#

As the distance between the radii is #<# than the sum of the radii. the circles overlap.

The greatest disnce is #=12.2+17=29.2#

graph{((x+3)^2+(y-5)^2-64)((x-7)^2+(y+2)^2-81)=0 [-28.85, 28.87, -14.43, 14.45]}