Two circles have the following equations: #(x +2 )^2+(y -5 )^2= 16 # and #(x +4 )^2+(y +7 )^2= 25 #. 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 · 2016-12-23T05:15:09

No overlapping-
Greatest distance #=21.17#

We calculate the distance between the centers of the circles and we compare this to the sum of the radii.

The centers of the circles are #(-2,5)# and #(-4,-7)#

The radii are #=4# and #=5#

Distance betwwen the center is

#d=sqrt((-4--2)^2+(-7-5)^2)#

#d=sqrt(4+144)=sqrt148=12.17#

The sum of the radii is #s=4+5=9#

Therefore,

#d>s#

So the circles do not overlap.

The greatest distance is #=s+d=9+12.17=21.17#

graph{((x+2)^2+(y-5)^2-16)((x+4)^2+(y+7)^2-25)(y-5-6(x+2))=0 [-31.47, 33.5, -13.18, 19.28]}